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2009 ASSESSMENT OF THE DELAWARE BAY

BLUE CRAB (Callinectes sapidus) STOCK

Richard Allen Wong

Delaware Division of Fish and Wildlife

Department of Natural Resources & Environmental Control

89 Kings Highway

Dover, DE 19901

December 8, 2009

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EXECUTIVE SUMMARY

The blue crab (Callinectes sapidus) is the most valuable commercial fishery species in

the State of Delaware. Harvest occurs from a residential Delaware Bay stock, which supports

fisheries in both Delaware and New Jersey. Between 1978 and 1995, bay-wide blue crab

commercial landings increased by 1,175% peaking at over 5.7 million kg (12.7 million lb).

Following a sharp decline in landings in 1996, the State of Delaware began efforts on a fishery

management plan and quantitative stock assessment to monitor the status of the stock. The

stock supported historically high levels of harvest for an extended period averaging 4 million

kg*y-1 (8.8 million lb) from 1988-2002. Landings again dropped significantly to less than 2 million

kg*y-1 (4.3 million lb) in 2003 and 2004 concomitant with a detected decline in stock abundance.

Depressed abundance was observed through yearly stock assessments for five years from

2002 to 2006. Some concern for the stock was raised given low adult abundance yet a rebound

in harvest to prior high levels of 3.4 million kg*y-1 (7.5 million lb) in 2005 and 2006. Recruitment

improved in 2006 and 2007, fueling an increase in 2007-2008 baywide landings to an above-

average level of 3.8 million kg (8.4 million lb).

This report provides results of the eleventh comprehensive stock assessment of the

Delaware Bay blue crab stock. The assessment employs a catch-survey population model that

simulates stock dynamics through time using two discrete groups of pre-recruited and fully

recruited individuals (Collie and Sissenwine 1983). The CSA model produces absolute

estimates of stock abundance and annual instantaneous rates of total mortality Z. Estimates of

abundance and total mortality were combined with known harvest to calculate a range of annual

exploitation rates µ. This range of µ was employed to generate upper and lower bounds of

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annual F rates. Stock status was assessed relative to F-based benchmarks (Frep =1.3, Fmax

=1.0, F0.1 =0.6, F = M = 0.8), and from an index-based measure of spawning stock biomass

(Helser and Kahn 1999). Separate combined-sex, male, and female CSA analyses were

completed.

Four different model configurations of varying error component weightings were explored

based on work by Kahn and Helser (2005). The four model configurations consisted of an

observation error-only model and three models with varying weightings of observation and

process error residuals. A preferred model was chosen that emphasized the fit to observed

abundance indices while minimizing the effect of process error. The mixed-error model with the

smallest process error weighting provided the best fit to observed indices by minimizing the

influence of the model difference equation in the prediction of indices. Reducing the influence of

the model difference equation was helpful since the model could not account for the effect of

density dependent mortality on pre-recruits apparent in recurring residual patterns.

The Delaware Bay blue crab stock can fluctuate wildly. Since 1978, model estimates of

annual blue crab abundance have ranged from 29 to 614 million, with a mean and median of

155 and 135 million crabs. Most of the fluctuation is caused by great variability in pre-recruit

numbers. Time series estimates of pre-recruit abundance ranged from 15 to 544 million, with a

mean and median of 124 and 95 million recruits. Pre-recruit abundance dropped to 35 million

crabs in 2008, among the lowest of the time series. Full recruit abundance ranged between 9

and 70 million crabs, with a mean and median of 31 million individuals. Terminal year full-recruit

abundance was 23 million, representing a substantial decline from 37 million crabs in 2007.

Terminal year (2007-2008) fishing mortality rate on the combined-sex stock was F =

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0.64, below all said reference points. Terminal F rose considerably from the prior year F =0.44.

The lower and upper bounds of terminal year F ranged from 0.35 to 1.22. The most-recent 3

year mean F was 0.71, approximately equal to benchmarks F0.1 and 0.8*M, with lower and upper

3 year means of 0.39 and 1.23. The 30 year mean F was 0.51 with upper and lower means of

0.28 and 0.78.

Additional fishery-independent indices of relative abundance portray a gradual recovery

in stock abundance after bottoming in 2002-2003. Low young-of-the-year abundance began in

2000 and continued with below-median YOY index values in four of the six ensuing years,

bottoming in 2002. Above-average winter mortality in winter 2002-2003 likely exacerbated the

effects of the weak 2002 year class. Depressed CPT values of recruits (medium crabs), large

crabs, and spawning stock were observed from 2003-2006. Harvest was depressed in 2003

and 2004 concomitant with the deterioration in stock abundance. Harvest rebounded

considerably in 2005 and 2006 amidst the ongoing low levels of recruitment and adult

abundance likely prolonging the depression in stock abundance. In 2006, YOY recruitment

spiked spurring a recovery to above-average values in medium and spawner indices in 2007. In

2008, however, the YOY index was very poor, which may act to stall the observed recent stock

recovery.

Despite low levels of abundance from 2003-2006, the stock still persisted at or above its

spawning stock biomass threshold. The stock exhibits very strong resiliency at low spawning

abundances and depensation at high abundances given a Ricker stock-recruitment relationship.

An example of its resiliency was seen in a large spike in YOY abundance in 2006 after only

small incremental increases in low SSB beginning in 2004. Spawning stock levels observed in

2008 should yield near optimal recruitment in 2009 given the S-R relationship.

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In the terminal model year we observe low blue crab abundance and high fishing

mortality rates. Terminal estimates of absolute abundance are below-average for both pre-

recruits and full-recruit crabs. Recent fishing mortality rates are at high levels above time series

norms and near upper management thresholds. Furthermore, a weak year class was observed

in terminal year 2008 which forecasts poor fishery recruitment into exploitable stages in 2009.

On the other hand, the stock has shown very high resiliency/productivity at observed low

abundance levels. The standing spawning stock in 2008 is at a level that should produce robust

juvenile recruitment in 2009. This is encouraging for a rebound in year class strength in 2009

and exploitable abundance in 2010.

This work portrays a highly resilient stock under substantial exploitation pressure. Stock

status in the terminal year in terms of abundance and F is below-average, yet these metrics

should rebound in the near future given an expected recovery in recruitment.

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Executive Summary .................................................................................................................... - 3 -

Background ................................................................................................................................. - 9 -

Life History ................................................................................................................................ - 10 -

Distribution ....................................................................................................................... - 10 -

Early Life History .............................................................................................................. - 11 -

Age and Growth ............................................................................................................... - 12 -

Maximum life span........................................................................................................... - 16 -

Reproduction and Maturity .............................................................................................. - 16 -

Predator Prey Interactions ............................................................................................... - 17 -

Natural Mortality ............................................................................................................... - 18 -

Unit Stock Definition ........................................................................................................ - 19 -

Fishery Description ................................................................................................................... - 20 -

Overview .......................................................................................................................... - 20 -

Commercial Fishery Harvest ........................................................................................... - 21 -

Sex-specific harvest ................................................................................................... - 24 -

Recreational Fishery........................................................................................................ - 25 -

Data Sources ............................................................................................................................ - 26 -

Harvest ............................................................................................................................ - 26 -

Commercial Landings ................................................................................................. - 26 -

Recreational harvest ................................................................................................... - 27 -

Fishery-Independent Data ............................................................................................... - 28 -

Indices of Abundance ................................................................................................. - 28 -

Instantaneous Natural Mortality Rate .............................................................................. - 29 -

Methodology .............................................................................................................................. - 29 -

Population Model ............................................................................................................. - 29 -

Model Inputs ............................................................................................................... - 33 -

External-Model Calculations of Fishing Mortality ............................................................ - 36 -

External Indices of Relative Abundance ......................................................................... - 37 -

Index-Based Stock–Recruitment Model .......................................................................... - 38 -

Results ...................................................................................................................................... - 38 -

Error-weighting Model Selection ..................................................................................... - 39 -

Combined-Sex Model ...................................................................................................... - 41 -

Model Outputs ............................................................................................................ - 41 -

Mortality Rates ............................................................................................................ - 42 -

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Indices of Relative Abundance........................................................................................ - 43 -

Index-Based Stock Recruitment Model ........................................................................... - 44 -

Discussion ................................................................................................................................. - 45 -

Stock Status .................................................................................................................... - 47 -

Acknowledgments ..................................................................................................................... - 49 -

References Cited ...................................................................................................................... - 51 -

Tables ....................................................................................................................................... - 61 -

Figures ...................................................................................................................................... - 70 -

Appendix I ................................................................................................................................. - 89 -

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BACKGROUND

The blue crab (Callinectes sapidus) is the most valuable commercial fishery resource in

the State of Delaware. Its landings value is more than two times greater than all of Delaware‟s

commercial fisheries combined. Given its importance, the State of Delaware monitors

commercial blue crab landings and relative stock abundance to complete a yearly quantitative

stock assessment with federal funding provided by the Atlantic Coastal Fisheries Cooperative

Management Act. This report represents the eleventh comprehensive assessment of the

Delaware Bay blue crab stock, providing estimates of stock size and fishing mortality rates from

1978 to 2008.

The Delaware Bay Blue Crab Fishery Management Plan was prepared by the State of

Delaware in cooperation with the State of New Jersey in 1999 amidst an uneasy period of ten-

plus years of increasing commercial effort and harvest in the bay. A sharp decline in landings in

1996 after a historically unprecedented peak in 1995 was feared to be a potential signal of stock

decline due to overfishing (Helser and Kahn 1999). A quantitative assessment employing a

stage based, catch-survey approach (Collie and Sissenwine 1983; Conser and Idoine 1992) was

completed in 1999 revealing fishing mortality rates (F) on the stock to be near the upper

management target (Fmax) indicating a fully-exploited stock (Helser and Kahn 1999). Annual

fishing mortality rates had exceeded the management threshold Frep in several years between

1985 and 1995, prompting management recommendations to prevent further fishery expansion

(DDFW 1999).

Updates and improvements to the quantitative assessment have occurred annually since

1999. A stochastic decision-based framework that incorporated statistical uncertainty

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associated with both terminal year F and the derived biological reference point, in order to

generate an overfishing probability was included in the 2000 assessment (Helser 2000; Helser et

al. 2001). In 2003, an alternative method for calculating fishing mortality was explored, based on

a derivation of the catch equation using model-estimated stock size and known harvest to

calculate annual F (Kahn 2003). The 2005 assessment included a reanalysis of historic

landings allowing the indices of abundance to occur at the start of the harvest year (Wong and

Kahn 2005). Assessments from 2006 to 2008 explored sex-specific growth rates, indices of

abundance, and landings for modeling population dynamics of male and female segments of the

Delaware Bay stock separately (Wong 2006; 2007; 2008).

This report represents the eleventh comprehensive assessment of the Delaware Bay

blue crab stock. A continued investigation of harvest, abundance, and population dynamics is

covered in the report. Stock status is assessed by measuring model outputs relative to F-based

benchmarks and by examining current trends observed in several fishery independent relative

abundance indices.

LIFE HISTORY

Distribution

The blue crab (Callinectes sapidus) is a member of the swimming crab family Portunidae,

and inhabits primarily estuarine habitats throughout the western Atlantic, Gulf of Mexico, and

Caribbean, from Nova Scotia (although rare north of Cape Cod) to northern Argentina, and

along western South America as far south as Ecuador (Williams 1979). Its range overlaps with

the closely related lesser blue crab (C. similis) in Delaware Bay. However, the primary

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distribution of the lesser blue crab is south of Cape Hatteras, NC (Gosner 1978), making it only

an occasionally observed species in Delaware Bay.

Early Life History

Blue crab spawning occurs in the summer months in lower Delaware Bay with peak larval

abundance occurring in August (Dittel and Epifanio 1982). Larvae are exported from the estuary

into the coastal ocean where they undergo a 3-6 week, seven stage zoeal development in

surface waters (Epifanio 1995; Nantunewicz et al. 2001). Quantitative models describe an initial

southward transport of zoeae along the inner continental shelf within the buoyant estuarine

plume after exiting the estuary (Epifanio 1995, Garvine et al. 1997). Northward transport back

toward the estuary is provided by a wind-driven band of water flowing northward along the mid-

shelf. Across-shelf transport into settlement sites in Delaware Bay is accomplished by coastal

Ekman transport tied to discrete southward wind events (nor‟easters) in the fall. These discrete

wind events may have a large effect on larval recruitment and settlement success in the bay and

strongly influence year class strength through juvenile and adult stages.

A single megalopal stage follows the seven stages of zoeal development. Megalopae

settle in lower Delaware Bay during the late summer and early fall where they utilize extensive

detritus beds as nursery habitat (DDFW 1998). Early crab stages (5-10 mm carapace width

(CW)) of both sexes begin an up-estuary migration to shallow areas of low to intermediate

salinity (Olmi 1995). Larger juvenile males tend to utilize lower salinity, more upper estuary

nursery areas, while juvenile females remain in the mid- to lower estuary during summer and fall

months (Miller et al. 1975). By winter, juveniles of both sexes appear to utilize middle to upper

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bay winter habitats and are not found in lower bay areas with overwintering adult females

(DDFW 1999). Both immature and mature crabs overwinter in a quiescent state in the sediment.

Age and Growth

Blue crab growth is discontinuous, occurring only during stepwise molting events

(ecdysis). Growth during each molt (molt increment) and molt frequency are therefore the sole

components of growth rate. Molt frequency decreases with size, ranging from 3-5 days as

larvae to 20-50 days for large adults during the growing season (Guillory, unpublished). Molt

frequency also decreases during the winter, with cessation in molting occurring below 13C for

juveniles (Guillory, unpublished). Number of molts is determinate at about 25 over a lifetime

(Newcombe et al. 1949; Van Engel 1958), so maximum size is ultimately a function of the

cumulative incremental growth per molt (Leffler 1972). Females exhibit a terminal molt at

maturation (pubertal molt), and are estimated to have fewer post-megalopal stage molts (18)

than males (20) (Newcombe et al. 1949). Post-puberty ecdysis in females has been

documented, but is considered a very rare occurrence (Guillory et al. 2001). According to

several watermen in Delaware Bay mature females (sooks) have occasionally been found in

peeler condition, but had always died in the molt when held in captivity (Kahn 2003).

Blue crab growth in Delaware Bay is described in earlier assessments from modal

progression analyses of size distributions observed in monthly sampling by the Delaware

Division of Fish and Wildlife‟s (DDFW) juvenile crab and finfish trawl survey. The following

description of growth is taken from Helser and Kahn (1999) and Coakley‟s (2004) examinations

of monthly width-frequency distributions during the periods of 1979-1981 and 1980-1981,

respectively.

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New recruit blue crabs appear in trawl samples in August. In Coakley‟s (2004) width-

frequency analysis, mean cohort sizes of new recruits in August of 1980 and 1981 were 24.2 ±

7.9mm and 29.5 ± 8.1mm, with individuals ranging in size from about 5 to 50 mm CW. The age

1+ crabs in August of 1980 and1981 (the previous year‟s recruits) had mean cohort carapace

widths of 137.8 ± 17.5 mm and 130.0 ± 32.4 mm, and individuals ranged in size from about 75 to

190 mm CW. Similarly, Helser and Kahn (1999) reported the August size range of age 1+ crabs

from 65 to 175 mm CW in 1979 (Figure 1). According to Helser and Kahn (1999), new recruits

reach an upper size range of 80-90 mm CW during their first September, already overlapping

with sizes of small age 1+ crabs (Figure 1). By October, largest sizes of new recruits reach 100

mm CW (Helser and Kahn 1999) (Figure 1). By the following May, fast growing new recruits are

near 100 mm CW or higher, mixing in size with age 1+ crabs (Helser and Kahn 1999) (Figure 1).

By July (at approximately one year of age), the mode for age 0 is roughly 60 mm, although

some have probably passed 120 mm (Helser and Kahn 1999). By their second August, when

the new year class appears, the new age 1 crabs have merged with older crabs with a mode of

135 – 150 mm CW, and by September, nearly all age 1 crabs have reached a size greater than

100 mm (Helser and Kahn 1999) (Figure 1). In October of 1980, sizes of new recruits and older

crabs were mixed forming a single broad size distribution (Helser and Kahn 1999) (Figure 1). In

June of the following year (1981), there was virtually a unimodal distribution with a mode of 80

mm and by July 1981 crabs had grown larger to a mode of about 115 mm CW (Helser and Kahn

1999) (Figure 1). By August 1981, the large majority of age 1+ crabs were 120 mm or greater, as

new recruits again appeared in the survey (Helser and Kahn 1999) (Figure 1).

Helser and Kahn (1999) further generalized their growth observations using size stages,

small, medium, and large, as growth milestones. Recruits begin to reach the medium stage (60-

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119 mm CW) in October, and the large stage (>119 mm) by the following June (Figure 1). By

July, hard crab landings usually increase as more age 0 animals recruit into the legal size (127

mm in DE, 120 in NJ). The overwhelming majority of the cohort reaches the large stage by the

end of their second October, with new recruits overwintering as mediums. This proportion varies

among years. Kahn et al. (1998) substantiated this description of blue crab growth using life-

stage-specific indices of abundance to predict later life stages.

Von Bertalanffy (LVB) growth parameters were estimated by Helser and Kahn (1999)

from the modal analyses of monthly width-frequency data using MULTIFAN (Fournier et al.

1991). Three sets of LVB growth parameters were produced from three separate linear time

series of trawl data, each consisting of 21 monthly size distributions. Three cohorts were able to

be detected in the analysis. The final sets of growth trajectories did not necessarily represent

the best model fit to the data among numerous runs (Helser and Kahn 1999), as interpretation

was needed to weigh model fit with realistic biological outcomes (ostensibly due to the quick

growth and ambiguity in discerning cohorts at larger sizes). The predicted growth trajectories of

crab carapace width as a function of age for the three sets of parameters are shown in Figure 2.

Growth scenario 1 (K=0.75, L =234.7) was accepted for the purposes of their subsequent yield

per recruit analysis.

Subsequent examinations of monthly width frequency distributions from the DDFW trawl

survey revealed expected differences in growth between male and female blue crabs (Figure 3)

(Wong 2006). Wong (2006) estimated non-seasonal and seasonal LVB parameters from sex-

specific datasets of width frequency distributions across 26 months from 1996-2000 using a

version of the Elefan method (Pauly 1987) from the Length Frequency Distribution Analysis

software (LFDA). Seasonal growth was described by the equation: L(t) =Linf*(1-EXP(-(k*(t -

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t0)+(C*k/2 )*Sin(2 )*(t-ts)-(C*k/2 )*Sin(2 )*(t0-ts)) (Hoenig and Hanumara 1982). Allowing for

seasonal depressions in growth in the LVB curve was helpful in better fitting the male size

frequency data (C =0.975), but did not necessarily improve the fit to the female data (C =0.1).

Two sets of sex-specific growth parameters are presented below, representing the best

realizations of growth from the data:

Although there was model convergence around these estimates in fitting the given data,

the accuracy of the estimates could not be evaluated. Given fast growth and the fairly rapid

disappearance of size distinguishable cohorts, other methods aside from size frequency analysis

should be explored to produce alternative growth curves for the stock.

While males and females exhibited similar early growth rates based on the seasonal

growth curves, males clearly attained a larger maximum size than females (Figure 3). Of

158,849 blue crabs captured in the DDFW 16 ft. trawl survey since 1978 the maximum size

observed was 230 mm CW (n=2, unidentified sex) with only six total specimens greater than or

equal to 200 mm. Since the onset of sex identification of crabs by DDFW in 1995, only one

female was observed greater than 180 mm, while 14 males were greater than 180 mm,

suggesting that the two 230 mm specimens were most likely males.

Males 1 Males 2 Females 1 Females 2

Linf 261.077 203.96 191.767 167.231

k 0.576 0.562 0.703 0.675

T0 -0.02 -0.74 -0.18 -0.6

C 0.975 0.922 0.1 0.036

Ts -0.137 0.141 0.19 -0.2

Score 0.17136 0.158 0.177 0.1846

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Maximum life span

Van Engel (1958) indicated the general lifespan to be two to three years. Kahn (2003)

postulated that rapid growth and early maturation (1 year) of blue crabs are not consistent with

longer lived decapod crustaceans such as snow crabs, king crabs, and American lobsters.

Helser and Kahn (1999) assumed a four year maximum age for the mixed-sex Delaware Bay

stock. Mature females initially tagged in the Chesapeake (Rugolo et al. 1998) and in North

Carolina (Fischler 1965) were returned by fishermen after several years, possibly indicating a

lifespan of up to 8 years (Rugolo et al. 1998; Miller and Houde 1998). However, possible biases

related to public-generated tag returns are often cited with respect to these cases (Kahn 2003).

Recent fishery-independent tag-recapture work in the Chesapeake indicated at least a 4 year

lifespan for females, given an at-large period of 3 years for a tagged mature female (Lambert et

al. unpublished; pers. comm. R. Aguilar, Smithsonian Environmental Research Center).

Reproduction and Maturity

Females mate immediately after their pubertal molt into sexual maturity, usually late in

their first year (summer). Females then store the sperm over the winter and produce eggs in the

following summer at the end of their second year. Prager et al. (1990) estimated fecundity per

batch as over 3x106 eggs. Females may spawn twice in their first year of spawning (Churchill

1921; Van Engle 1958). Some researchers believe it is possible for females to spawn into their

fourth summer as age 3 (Kahn 2003). However, Cole and Beck (1975) observed evidence of

previous spawning (i.e. presence of nemertean egg parasite) on only 4.5% of overwintering

females in Delaware Bay.

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Maturation by carapace width of Delaware Bay blue crabs was estimated from a sample

of 1,335 female crabs collected from the commercial catch between 1995 and 1997 (Helser and

Kahn 1999). Female blue crabs were categorized as either mature or immature, based on the

shape of the crab‟s apron, and modeled as a binary response using a logistic regression model

(Agresti 1990):

logit (P) = log (P/(1-P)) = α + β*CW + ε

where: P = Pr(Y=1|X) is the response probability, CW = carapace width (mm) and α, β

are parameter estimates. Observed maturity by carapace width and the predicted maturity ogive

are shown in Figure 4 (Helser and Kahn 1999). Results were similar to those of Rothschild et al.

(1992) who found very few mature crabs with carapace widths of less than 100 mm, and nearly

all crabs were fully mature by 140 mm.

Predator Prey Interactions

Juvenile and adult blue crabs hold an important ecological role as opportunistic benthic

omnivores, with major food items including bivalves, fish, crustaceans, gastropods, annelids,

nemertean worms, plant material, and detritus (Guillory et al. 2001). Post-settled blue crabs

have been shown to have a key effect on infaunal community structure, particularly through

major predation on bivalves such as the eastern oyster (Crassostrea virginica) (Eggleston 1990),

Mercenaria mercenaria (Sponaugle and Lawton 1990), Rangia cuneata (Darnell 1958), Mya

arenaria (Blundon and Kennedy 1982; Smith and Hines 1991; Eggleston et al. 1992), and other

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bivalve species (Blundon and Kennedy 1982), and through indirect mortality on infaunal species

from mechanical disturbance of sedimentary habitats caused by foraging (Virnstein 1977).

Fish appear to be the primary predators on blue crabs, with more than 60 fish species

listed as known predators (Guillory et al. 2001). Blue crabs are known to be a common

component of both juvenile and adult striped bass in Chesapeake Bay, albeit with great

variability in relative importance among studies (Speir 2001). Although there have been recent

investigations on the potential negative effect of the recovered striped bass stock on the

Chesapeake Bay blue crab stock, no connection with decreasing blue crab population numbers

has been supported (Booth and Martin 1993; Speir 2001).

Another very important source of predation on blue crabs occurs from cannibalism, as

cannibalized blue crabs make up as much as 13% of the diet (Darnell 1958). Cannibalism

appears to increase with increasing crab predator size and is heaviest during the period of

juvenile recruitment (Mansour 1992). Peery (1989) demonstrated that size specific cannibalism

occurs, with small crab predators preying on small juveniles, and large crabs selecting the upper

size range of juveniles. However, with high abundance of small juveniles, large blue crab

predators also cannibalized small sizes, suggesting strong density-dependent regulation of

juveniles (Peery 1989).

Natural Mortality

A high rate of natural mortality is assumed to occur on the Delaware Bay stock given the

presumably short, 3-4 year life span of individuals. A range of instantaneous natural mortality

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rates (M) for the stock was explored in previous DDFW assessments, varying from 0.375 to 1.1.

Helser and Kahn (1999) adopted M =0.8 as the input for natural mortality rate for the CS

assessment model assuming the maximum age between 3 and 4 for Delaware Bay blue crabs

and using the convention, ln(5%)/maximum age. This M was maintained in the yearly

assessments from 1999-2007 excluding 2004. Coakley (2004) chose M =0.75 for the final

model output after testing sensitivity of model outputs to ranging M values from 0.375 to 0.75

(based on maximum ages of 4, 6, and 8). Rugolo et al. (1997) employed the 5% max age

convention, assuming a maximum longevity of eight years based on aforementioned tag returns

in Chesapeake Bay, yielding M =0.375. Helser and Kahn (1999) also investigated natural

mortality by regressing an apriori length-based estimate of total mortality (Z) as a function of

fishing effort (Gulland 1983). Natural mortality (M) was calculated as 0.84 to 1.1, albeit with

some recognized uncertainty in both measures of fishing effort and the length-based estimates

of Z.

Unit Stock Definition

The unit stock of this assessment is defined as all blue crabs that spawn in and utilize

the tidal and non-tidal waters of Delaware Bay. The significant stock-recruitment relationship

observed in Delaware Bay, estuary-retentive coastal circulation patterns for larval transport, and

the considerable distance of Delaware Bay to other large estuaries suggests the stock is the

primary source of its own recruits. However, some degree of stock mixing between estuaries

along the mid-Atlantic and south-Atlantic Bights occurs, given the larval emigration into the

coastal shelf before re-entering the estuary to settle. Electrophoretic allozyme analysis of blue

crabs (N=750) from 16 near-shore locations from New York to Texas indicated substantial gene

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flow among sites, however, with genetic structuring occurring (McMillen-Jackson et al. 1994).

FISHERY DESCRIPTION

Overview

The Delaware Bay blue crab stock is harvested by commercial and recreational fisheries

of Delaware and New Jersey. On average, 2.8 million kg (6.2 million lb) of blue crabs are

harvested annually from the Delaware Bay by commercial and recreational crabbers since 1973,

with 52% of the total weight landed in the State of Delaware (DNREC data; NMFS data) (Table

1; Figure 5). The commercial fishery is responsible for the majority of total annual harvest.

Recreational harvest estimates were about 4% and 20% of the hard crab pot landings in

Delaware and New Jersey.

Total annual Delaware Bay blue crab landings increased by 1,175% from 1978 to 1995

causing concerns of overfishing and the development of fishery restrictions in both states. Total

landings peaked at 5.4 million kg (11.9 million lb) in 1995, remained high for the next seven

years (averaging 3.7 million kg), and then declined considerably in 2003 and 2004 (1.7, 2.3

million kg). Recent landings have rebounded again to historical high levels, averaging 3.4

million kg*y-1 from 2005-2007, and reaching 4.1 million kg in 2008 (Table 1).

Differing size regulations exist between states. The commercial fishery minimum size for

male hard crabs is 5” (127 mm) CW in Delaware and 4 ¾” (120 mm) CW in New Jersey.

Female hard crabs must be mature for commercial sale in Delaware with no minimum size limit,

whereas female hard crabs must be both mature and greater than 4 ½” (114.3 mm) CW in New

Jersey. Gravid (sponge) females are protected from harvest in both states. Recreational size

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limits and female maturity requirements are the same as commercial regulations in Delaware.

Both male and female hard crabs carry a uniform minimum size limit of 4 ½” CW in New Jersey

for recreational harvest. The recreational harvest limit is one bushel per person per day in both

states.

Commercial Fishery Harvest

Blue crabs easily make up the highest value commercial fishery in the State of Delaware,

with a 2008 ex-vessel value of 5.3 million dollars, and a combined New Jersey and Delaware

value of 10.6 million dollars. The majority of the commercial landings occur in the warmer

months from May to September (75% of annual total) with a peak in August, during the period

when the pot fishery traditionally harvests mostly male hard crabs (Figure 6). Four distinct

market categories are recognized in Delaware: large male hard crabs (#1 crabs, a.k.a. jimmies),

small male hard crabs (#2 crabs), female hard crabs (#3 crabs), and peelers (crabs about to

molt). Helser and Kahn (1999) assumed peeler landings to be entirely immature females about

to molt into maturity.

Commercial landings are prosecuted by two fisheries, a winter dredge fishery and a

spring-to-fall pot fishery that harvests the lion‟s share of annual landings. Ninety-one percent of

Delaware and New Jersey Delaware Bay commercial hard crab landings (kg) are annually

harvested by pots (2003-2008) (Tables 2, 3).

The pot fishery typically begins in April or May with increasing activity of mature,

overwintering females prior to June egg production known as the “sook run”. Substantial spring

landings composed mostly of #3 crabs (female hard crabs) occur in May based on this sook run

- 22 -

(Figure 6). As sooks produce eggs and become sponge crabs, they are protected from harvest

resulting in the movement of crabbing effort further up-bay and away from higher salinity areas

inhabited by gravid females. Landings of mature males increase in July and peak in August or

September as new recruits enter the fishery. In the 1990s, increased targeting of females during

their migration down bay in September and October was noted, ostensibly driven by added

Asian export and western U.S. demand (Cole 1998); however, this trend has not continued in

recent years. By November, the pot fishery season has ended.

Peelers make up 3.8% of annual pot landings (numbers) in Delaware (2003-2008).

Significant peeler landings occur in June, or some years in May, occurring primarily around the

new and full moons. Peelers are typically held until molting occurs and sold as soft crabs for

their high market value, and to a lesser degree as fishing bait. In the 1990s, crab pots began to

be modified with 1” mesh (previously 1 ½”) to target peelers. Peeler pots are baited with a

mature male (jimmy) to attract females seeking males for protection during ecdysis and for

mating immediately after the molt. Total (combined Delaware and New Jersey) peeler landings

peaked in 1995 at 6.15 million peelers (580,959 kg) and have since declined to 1.14 million

crabs (107,434 kg) in 2008.

In an effort to curb fishing effort in 1994, both Delaware and New Jersey limited entry into

their commercial crab pot fisheries by capping the number of annual pot licenses sold at the

1994 level, specifying future license targets of 82 and 312 annual licenses for the bay. Pot

fishery licenses have declined by 40% in New Jersey through attrition since peaking in 1994

(Table 4). Delaware pot licenses have remained at the 1994 level. If or when annual licenses

eventually fall to 82 in Delaware, a special lottery will be held to increase the license total to 100.

The pot fishery season is restricted to March 1 to November 30 in Delaware, and from April 6 to

- 23 -

December 4 in New Jersey (Delaware Bay only). Commercial crabbers are limited to 600 pots in

New Jersey. In Delaware, crabbers can renew a commercial license for up to 200 pots in

increments of 50. A Delaware vessel with three crab pot licenses assigned to it can fish a

maximum 500 pots.

The commercial dredge fishery is smaller in comparison to the pot fishery and operates

during a shorter, three to four month winter season. Commercial crab dredging is permitted from

December 15 to March 30 in Delaware, and November 15 to April 15 in New Jersey (Delaware

Bay only). The fishery is further restricted to specific portions of Delaware Bay and by gear

limitations on overall dredge length and numbers (2) per vessel. Twenty-three percent of the

Delaware dredge landings occur in December. Peak dredge landings (40%) occur in January,

and taper to 27% and 10% in February and March.

The dredge fishery primarily lands mature females (sooks) that have overwintered in

aggregations in the higher salinity areas of the lower bay. Unlike the pot fishery, males only

make up a small component (10% weight) of the annual dredge harvest (DDFW data). Market

grade composition does not change considerably across the relatively short dredge season.

In the late 1990s, New Jersey capped Atlantic coast commercial dredge fishery licenses

to the number of 1993 licenses (338). Annual dredge licenses have been well below this limit

since its cap inception. In 1997, New Jersey began issuing dredge licenses by water body.

Since 1997, New Jersey dredge licenses in Delaware Bay have fluctuated between 80 and 94

without trend (Table 4). Delaware dredge licenses have remained fairly constant since 1994

(Table 4).

- 24 -

Annual commercial landings are affected by severe winters in this region (Helser and

Kahn 1999). Unusually cold or stormy winters cause sharp decreases in dredge landings as

seen in 1978 and 1979. In severe winters, the commercial dredge fishery catches greater

proportions of dead adults indicating higher overwintering mortality. In 1996, the Delaware

Division of Fish and Wildlife (DEDFW) observed >30% mortality in commercial dredge catch

samples. Overall landings in the subsequent year (1997) declined by 40%.

Sex-specific harvest

Male and female components of the harvest were determined based on sex- and size-

based fishery market grades. For reference, large male hard crabs are sorted by the fisherman

in Delaware into market grade 1; small males are sorted as 2‟s; females are graded as 3‟s.

Market grades 1 and 2 were therefore assumed to be composed of 100% males for this

assessment. Market grade 3 and peelers were assumed to be 100% females. Fish house

sampling in 2006 corroborated these hard crab sex-ratios. The peeler fishery in Delaware

predominantly targets females during relatively short-lived pulses in the spring and summer.

Although the male proportion of peeler landings is likely minor compared to females, the true

ratio is unknown and in need of future investigation.

Market grade information of New Jersey landings was available beginning in 1999,

consisting of male, female, mixed, and peeler categories. Prior to 1999, all hard crabs were

recorded as mixed. Mixed NJ landings prior to 1999 were divided into male and female

components based on the Delaware sex-ratio observed in that specific year, gear, and month

combination. The year/gear/month DE and NJ sex-ratios were very similar from 1999 to current.

- 25 -

Gaps in sex-ratio data were filled with gear/month sex-ratios across years (1999-2006) observed

in NJ landings.

Most of the commercial harvest is composed of male crabs. Annual harvest is 64.7%

males in numbers and 60.4% males in weight in Delaware Bay since 2003. Males and females

were generally harvested in equal proportions until 1998 when the ratio of males became

consistently higher than females in Delaware Bay harvest (Figure 7).

Recreational Fishery

Estimates of recreational blue crab harvest in Delaware Bay are limited. Cole et al.

(1997), utilizing a bus route design on land to quantify effort and a riverine boat sampling

program to determine catch rates, estimated 135,193 and 130,464 crabs landed in 1996 and

1997 by Delaware-only recreational crabbers. This was 1.7% and 1.2% of the hard crab

landings harvested by the Delaware commercial pot fishery in those years. Fifty-four percent of

the recreational landings were captured by commercial style crab pots, while 46% were captured

by traditional, shore-based gears, presumably traps, lines, hand nets, etc. Most of the harvest

occurred on the weekends, and in August and September.

An estimate of recreational harvest in NJ in 2005 was 1.9 million crabs (ORC Macro

2006), equal to 20% of the NJ commercial non-dredge hard crab harvest occurring during that

same period (May-Oct). In 2005, ORC Marco estimated that 1,925,425 (CV =20.5) hard crabs

were harvested in New Jersey by recreational crabbers using a telephone and intercept survey

design (ORC-Macro 2006). Most of the effort (69% of total) and harvest (65%) occurred during

the Jul-Aug period of the May-Oct survey. Seventy-four percent of the harvest was captured by

- 26 -

boat rather than by land crabbers. Nearly 75% of the harvest was composed of males, while

79% of the female harvest was mature. The total 2005 recreational harvest in NJ equalled 20%

of the NJ commercial (non-dredge gears) hard crab landings occurring from May-Oct.

In 2008, ORC Macro estimated Delaware-only recreational harvest to be 416,381

(numbers), equal to 4.3% of the Delaware commercial pot hard crab harvest. The sex-ratio was

6:1 males to females. Seventy percent of the female harvest was mature. Sixty-eight percent of

the harvest was caught by boat crabbers. All harvest was composed of hard crabs (no peelers).

Other estimates of recreational hard crab harvest are widely variable (expressed as

percentages of commercial production): 5.9% in Galveston Bay, TX (Benefield 1968); <4% in

Mississippi (Herring and Christmas 1974); 20% in Alabama (Tatum 1982); and 4.1% in

Louisiana (Guillory 1998).

DATA SOURCES

Harvest

Commercial Landings

Commercial fishery blue crab landings from Delaware and New Jersey were utilized in

the assessment covering the period 1978-2008. Annual Delaware landings were compiled from

multiple data sources: annual reports assembled by DDFW for the period 1978-1984; landings

data collected by a DDFW fishery-dependent dockside intercept survey for the period 1985-

2002; and mandatory, monthly, logbook reports submitted by commercial fishermen to the State

of Delaware for the period 2002-2008. Fisherman logbook reports and the DDFW dockside

intercept survey occurred simultaneously from 1985 to 2003. The DDFW survey suggests

- 27 -

possible under-reporting in fishermen logbook reporting from 1989 to 1994. However, good

agreement between fishermen logbook landings and survey landings began in 1995,

contributing to the decision to eliminate the DDFW survey in early 2003 (Figure 8). New Jersey

landings data were taken from the National Marine Fisheries Service commercial landings

statistics database from 1978 to 2000 and directly from fisherman logbook reports compiled by

the New Jersey Bureau of Marine Fisheries for 2001-2008.

Commercial landings reported in bushels were converted to numbers for use in the

assessment model. Bushels-to-numbers conversions were based on DDFW at-sea sampling of

pot and dredge landings in 1996 (unpublished DDFW data) (Table 5). Numbers per bushel by

market grade and gear (pot or dredge) were calculated from this DDFW sampling. Converting

bushels of unspecified market grade landings to numbers for the assessment required creating

conversions based on the known DDFW at-sea conversions weighted by empirical market grade

compositions observed in Delaware logbook landings.

Recreational harvest

Recreational harvest was estimated as a percentage of the annual, commercial non-

dredge, hard crab landings. A harvest proportion of 2.5% of the commercial non-dredge hard

crab landings was continued from earlier assessments to estimate yearly Delaware recreational

harvest from 1973 to 2007 (Helser and Kahn 1999). The 2008 recreational harvest estimate of

416,318 (approximately 4% of the commercial hard crab pot landings) was used in lieu of the

2.5% proxy. Annual recreational harvest in New Jersey was calculated as 20% of the

commercial non-dredge May-Oct hard crab landings based on the findings of the 2005 ORC-

Macro Delaware Bay blue crab recreational fishery survey (ORC-Macro 2006).

- 28 -

Fishery-Independent Data

Indices of Abundance

The Delaware Division of Fish and Wildlife has operated a blue crab and juvenile finfish

trawl survey in Delaware Bay since 1978. The 16 foot trawl is equipped with 1.5 inch mesh with

a 0.5 inch cod end liner. Fixed sites are sampled on the western inshore areas of the bay into

the Delaware River. Sites are sampled monthly from April through October with ten minute tows

against the tide. Blue crabs are measured in 5 mm increments, sexed, and counted.

Indices of pre-recruited and fully-recruited blue crabs were used in the assessment

model. Trawl data used for these indices were taken from the lower 26 stations that have been

sampled continuously since 1978 (Figure 9), and restricted to the August-September sampling

period (Helser and Kahn 1999). The index of pre-recruits was composed of the geometric mean

catch per tow (GM CPT) (in numbers) of blue crabs less than 120 mm CW. The index of fully-

recruited blue crabs was composed of blue crabs greater than or equal to 120 mm CW.

Other stage-specific indices of abundance have been developed from the trawl survey

for monitoring the stock yet not used in the population model. A YOY index is developed from

the GM CPT of small crabs (< 60 mm CW) in September-October. A second index, termed the

recruitment index in previous assessments, uses the GM CPT of medium crabs (60 mm CW –

119 mm CW) in the April – August period. An index of large crabs (GM CPT of crabs ≥ 120 mm)

was also developed based over the entire survey year (Apr-Oct).

Kahn et al. (1998) also developed measures of spawning stock biomass from the trawl

- 29 -

survey. The index of spawning stock consists of the arithmetic mean CPT (AM CPT) of large

crabs (≥ 120 mm) in spring tows (April and May). A similar, female only, biomass-based index

consists of the arithmetic mean tow weight (kg). Individual weights were calculated from

carapace widths using the female width-weight model from Rothschild et al. (1992):

Weight = (3.4865 X 10-3 * CW2.116) /1000.

Instantaneous Natural Mortality Rate

A constant instantaneous natural mortality rate of M =0.8 was utilized in the current

assessment model consistent with previous DDFW assessment methodology from 1999-2003,

and 2005-2006. A previous exploration of M included the regression of an apriori length-based

estimate of total mortality (Z) as a function of fishing effort by Helser and Kahn (1999) as per

Gulland (1983). Natural mortality (M) was calculated as 0.84 to 1.1, albeit with recognized

uncertainty in both measures of fishing effort and the length-based estimates of Z. Coakley

(2004) used a constant natural mortality rate of M =0.75 in the 2004 DDFW assessment.

Rugolo et al. (1997) estimated M =0.375, assuming a maximum longevity of 8 years based on

reportedly controversial tag returns in Chesapeake Bay.

METHODOLOGY

Population Model

The catch-survey population model simulates stock dynamics through time using two

size groups: pre-recruits and fully recruited blue crabs (Collie and Sissenwine 1983). Minimum

- 30 -

data requirements for the model include: 1) annual indices of population abundance (in

numbers) for each size stage (i.e., pre-recruit and fully-recruited sizes); 2) relative selectivities of

size stages to the survey gear; 3) annual total harvest in numbers; and 4) an estimate of

instantaneous natural mortality rate. The analysis was executed using the Collie-Sissenwine

Analysis (CSA) version 3.04 application from the NFT toolbox (version 2.11A). The catch-survey

model is based on the first order difference equation:

e )C - R + N(= N-M

yy0y01+y0, ,, (1)

which relates the fully-recruited stock size at the beginning of the year (N0,y+1), to the fully-

recruited stock size at the beginning of the previous year (N0,y), plus recruitment in the previous

year (R0,y), minus the catch (Cy), all discounted for natural mortality, M.

The above equation assumes that a pre-recruit is any crab smaller than the minimum

size vulnerable to the fishery at the beginning of the model year that will also become fully-

vulnerable to the fishery by the beginning of the next model year. The term, recruit, will be used

synonymously in place of pre-recruit for the remainder of this report. Helser and Kahn (1999)

defined recruit blue crabs to be less than 120 mm and fully-recruited crabs as greater than or

equal to 120 mm. The model year runs from September 1 to August 31. Helser and Kahn

(1999) offered three reasons for the size definitions and survey year: 1) current commercial

regulations specify a 120 mm and 127 mm minimum carapace width for hard crabs in New

Jersey and Delaware, respectively; 2) width frequencies indicate that the large majority of

recruits, which appear in the research surveys during August-September, have grown to the

fully-recruited size (120 mm) by the following year; and 3) Kahn et al. (1998) demonstrated a

significant positive correlation between large blue crab indices (defined as > 120 mm) in a given

year and pre-recruit size (< 60 mm) crab indices during the previous year. The catch-survey

model is predicated on the basis that a “signal” exists between recruit and fully-recruited sizes.

- 31 -

Given a September 1 to August 31 model year, the current model difference equation is

as follows:

e)] C - e)R + N[(= NM-0.

yM-0.

0y0y1+y0,2575 (3)

with the midpoint of harvest occurring at a point 75% into the survey year.

Survey indices of abundance are related to absolute stock sizes by

eNq = nt

0yny (4)

and

eRq = rt

0yry (5)

where r’y and n’

y are the observed research indices of recruit and fully-recruited blue crabs, q is

the catchability coefficient of the research survey gear, and eη t and eδ t are lognormally

distributed random variables, which represent survey measurement errors for the recruits and

fully-recruited indices, respectively. In essence, these errors represent the difference between

the observed survey indices of recruits and fully-recruited animals and the expected indices

predicted within the nonlinear least squares (NLLS) framework by the DeLury difference

equation. Another source of error, called process error, arises from the DeLury equation itself,

which is the difference between calculated indices of fully-recruited animals and the expected

value of the fully-recruited indices again predicted within the NLLS framework from the catch-

survey model.

Substituting the above equations into the model difference equation and including the

- 32 -

lognormally distributed process error (eε t):

e e]Cq - e)s/r+n[( = ntM-0.

1-ynM0.

r1-y1-yy2575 (6)

where

q / q = s nrr (7)

is the relative selectivity of recruits to the fully-recruited blue crab, set equal to unity. The

research survey uses a 1.5 inch mesh with a 0.5 inch codend liner (shrimp trawl) and it is

unlikely that small blue crabs of recruit size observed in the survey would escape at a rate

different from that of fully-recruited crabs.

Thus, the above equation is a statistically estimable function with 2Y parameters to be

estimated; ny for all years Y, ry for all years except the last year, and qn. Estimates of these

parameters (θ) are obtained by minimizing the least squares objective function (S):

2y

1-Y

y=1

2y

Y

y=1

2y

Y

2y=

+ + = )S( ˆ (8)

where λε and λδ are relative weights for the process error and recruit measurement error,

respectively (relative to the measurement error for indices of the fully-recruited size). Conser

(1995) describes an approach to weighting process and measurement errors within the least

squares objective framework that is implemented in this analysis to evaluate model sensitivity.

Four different model configurations were analyzed as in Kahn and Helser (2005), an

observation error-only (OE) model recommended by Collie and Kruse (1998) and three

configurations of a mixed error model, with the following weights of process error relative to

observation error: 1.0 equal weighting (EW), 0.5 (PE0.5), and 0.1 (PE0.1). The OE model

estimates q (catchability coefficient), the time series of the recruit index (except the last year‟s

value), and the full recruit index in the first year, for Y + 1 parameters. Model predicted full

- 33 -

recruit index values are calculated by the model difference equation (Eq. 6). All error

components were weighted equally. The mixed error models estimate q, all full recruit index

values, and all recruit index values except the last years‟, for 2Y parameters. Process error is

the difference between the full recruit index calculated by (Eq. 6) without the process error term

(i.e., deterministically with no error) and the full recruit index as calculated by (Eq. 6) with the

process error term included.

Given estimates of ny , ry, and qn from the nonlinear least squares minimization and the

value of relative selectivity, sr, population abundances for the recruit and fully-recruited blue

crabs are

Ny = ny /q

and

Ry = ry / sr q.

Annual estimates of spawning stock biomass were based on model estimates of

population abundance in numbers multiplied by the annual mean weight of adults observed in

the full recruit index of the DDFW trawl survey. Mean weights were converted from empirical

mean size (CW) of full recruits using the mixed-sex width-weight model,

Weight = (8.1636 X 10-3 * CW 2.43) / 1000,

from Rothschild et al. (1992)

Model Inputs

Indices

Annual indices of recruit and full-recruit blue crab abundance were constructed from the

- 34 -

DDFW juvenile finfish and blue crab trawl survey data. The combined-sex indices covered

years 1978-2008. Average weights of recruits and full-recruits were required by the NFT CSA

model. Average weight was based on empirical carapace width (CW) data from the survey and

the width-weight models from Rothschild et al. (1992):

Combined-sex: Weight = (8.1636 X 10-3 * CW 2.43) / 1000

Female: Weight = 0.0034865 * CW 2.1165

Male: Weight = 0.00022105 * CW 2.7208.

Model inputs are shown in Table 6.

Harvest

Annual harvest occurring over the model year (September to August) was also required

for the model (Table 6). Discard landings were input as nil given lack of discard sampling. The

discard component is likely minor given the pot fishery harvest practices. Average weight of the

harvest was calculated from the annual harvest weight divided by the total numbers of crabs

harvested. Combined-sex harvest inputs covered „model‟ years 1978-2007.

Methodological changes in quantifying baywide harvest occurred in 2005. A complete

re-analysis of historical Delaware and New Jersey landings was undertaken in 2005 in order to

synchronize annual harvest to a September-August model year, consistent with the timing of the

survey indices. Also prior to the 2005 assessment, New Jersey logbook-reported landings had

been inflated by 1.4 for hard crabs and by 2.3 for peelers on an annual basis, based on the

assumption of under-reporting in logbook records. Lower landings were observed in Delaware

fishermen logbooks versus the DDFW dockside intercept survey during the early years of those

overlapping methods. In the latter years of the dockside survey, however, both methods

- 35 -

produced very similar annual landings. In the 2005 assessment, New Jersey reported landings

were not expanded, given: better confidence in new, updated landings datasets provided by NJ

DEP; the uncertainty in assuming under-reporting of New Jersey landings based on logbook

versus survey differences in Delaware landings primarily based on the early part of the DDFW

dockside intercept survey; the inability to account for changes in under-reporting through time in

New Jersey; and based on recommendations from NJ Bureau of Marine Fisheries personnel

after extensive discussions (personal communication; T. Baum et al.). In addition to the uniform

expansion of New Jersey landings across years in previous assessments, some individual years

were also further increased to address abnormally low landings values. Delaware landings from

analogous time periods and gears were used as appropriate scalars in these situations. Given

new, updated landings datasets, these spot corrections to New Jersey landings were not

conducted in the 2005 assessment. Another methodological convention used in previous

assessments was the lagging of December dredge fishery landings, so that each December

harvest was counted towards the following calendar year. Ultimately, the updated landings

analysis for the current assessment produced slightly different landings totals from previous

assessments, although they are very similar in trend when viewed in the same time step (e.g.

calendar year) (Figure 10).

Instantaneous Natural Mortality Rate, M

Instantaneous natural mortality rate was fixed at M = 0.8, consistent with 1999-2003,

2005-2008 assessment methodology.

- 36 -

External-Model Calculations of Fishing Mortality

Annual instantaneous fishing mortality rate (F) was calculated from instantaneous total

mortality rate (Z), exploitation rate ( ), and annual percent mortality (A), derived from model

estimates of annual stock size. Total mortality (Z) is expressed as the log survival ratio:

N

R + N = Z

1+y0,

0y0y

eyN,R+ log (8)

A range of annual exploitation rates, , was calculated using the input catch in numbers divided

by exploitable stock size. Three estimates of exploitable stock size were calculated, providing

theoretical upper and lower bounds of exploitable abundance to account for the considerable yet

unknown amount of recruitment into the fishery occurring within the year due to fast growth of

pre-recruits (Kahn and Helser 2005). Given this unknown level of within-year recruitment, upper

and lower bounds around an estimate of exploitable stock size were created for calculating

exploitation rates and fishing mortality rates.

The best approximation of annual exploitable stock size, based on the method detailed

by Collie and Kruse (1998) was assumed to be R + N, decremented by natural mortality over the

time period until the harvest occurs

SC TTMeNR

harvest =

(a*)(

,

where R and N are the absolute abundances of pre-recruits and post-recruits, M =instantaneous

natural mortality rate, Tc = time when the harvest occurs, Ts = time when the survey occurs.

Maximum annual stock size was assumed to be R + N. Using a maximum estimate of

annual stock size yields a lower bound of exploitation rate,

- 37 -

)(b

NR

harvest= .

Minimum exploitable stock size was defined as the annual catch plus all post-recruits

surviving to the next survey year. Using a minimum estimate of annual stock abundance in the

following equation,

)( 1

c

tNcatch

harvest =

results in an upper bound of exploitation rate.

Fishing mortality is calculated by solving the catch equation for F,

F = Z/A,

where and Z are as defined and A is the total annual mortality as a percent,

At = (1 – Nt+1/ (Rt + Nt)) = (1 – e (–Z)).

External Indices of Relative Abundance

Stage-specific indices of abundance, other than the pre-recruit and full recruit indices

used in the population model, were analyzed to further describe population trends (Table 7).

These indices were drawn from the DDFW juvenile finfish and blue crab trawl survey and are

described in the previous section, Data Sources; Fishery-Independent Data; Indices of

Abundance.

- 38 -

Index-Based Stock–Recruitment Model

The index of recruits lagged by one year (see Data Sources; Fishery-Independent Data;

Indices of Abundance) was plotted as a function of the index of spawning stock biomass.

Recruits are defined as the medium crabs in April-August of the year following birth. Two stock

recruitment models were fit to the data by Helser and Kahn (1999). One model was a null model

with no density-dependent mortality (Fogarty et al. 1992). This is a simple regression of

recruitment on spawners with a linear term, a quadratic term and no intercept. The quadratic

term in the regression analysis was highly significant (p < 0.01) and substantially improved the

model fit (r2 = 0.62; p = 0.0002) over a model based on just the linear term (r2 = 0.38; p < 0.002).

Helser and Kahn (1999) rejected the null model of no compensation based on the linear

regression of recruitment on spawning stock. The standard Ricker model was then fit with an

additive normal error structure using the Marquardt algorithm in SAS. Based on the alternative

hypothesis of compensatory mortality for blue crabs, PROC NLIN in SAS was employed to fit the

nonlinear Ricker model, R = A*SSB*exp(B*SSB), where R is the estimate of recruitment, SSB is

the index of spawning stock biomass and A and B are model parameters. The coefficient of

determination, R2, is calculated as R27 of Kvalseth (1985): 1 - (residual SS/ uncorrected total

SS).

An index-based benchmark was determined from the S-R curve, equal to the SSB that

produces half of the maximum recruitment, termed the SSB50. This level of SSB has been

recommended as a measure of recruitment overfishing (Mace 1994).

RESULTS

- 39 -

Error-weighting Model Selection

An examination of error residuals revealed similar residual patterns across all four error-

weighting model configurations, revealing a difficulty of the model difference equation in

predicting observed index values in recurring circumstances. One noticeable residual pattern

was the under-prediction of recruits corresponding to years when very large observed recruit

index values occurred (Figure 11; Appendix I). Typical over-prediction of full recruit indices in

the year following large observed pre-recruit indices also occurred (Figure 12; Appendix I).

Another major source of residuals occurred when a low pre-recruit index and significant harvest

took place in the same year, yet a substantial full recruit index value was observed in the

ensuing year. This was particularly evident in 1990, when a weak, observed, recruit index and

considerable harvest occurred, yet the 1991 observed full recruit index was robust. Given the

model difference equation, low recruitment of individuals into the full recruit stage was expected

in the ensuing year.

These noticeable residuals fall into a larger, systemic pattern of a negative correlation

between recruit and full recruit index residuals. Observed full recruit index residuals are

negatively related to the previous year‟s recruit index residual (Figure 13). Typically, an

underestimated recruit index in a given year leads to the overestimation of the next year‟s full-

recruit index, and vice-versa. This is a somewhat natural consequence of the model difference

equation, since the model‟s calculation of full recruit abundance is based directly on the previous

year‟s recruit and full recruit abundance. However, it also indicates an inability of the model

difference equation to completely describe recruitment from one stage to the next, emblematic of

the model equation‟s inability to account for density dependent recruitment.

- 40 -

Recruit and full-recruit residuals were most pronounced in the observation error-only

(OE) and the equal-weight mixed error (EW) models, and were dampened as process error was

downweighted across the mixed error models. In this analysis of models, the model difference

equation is most heavily involved in the final convergence in the OE model, and declines in

importance as process error is downweighted across the mixed error models (EW, PE0.5, and

PE0.1). As influence of the model equation is reduced, there are less model constraints on

predicting the observed indices, allowing better agreement between observed and predicted

indices. One consequence to the increasing fit of predicted indices to observed indices is the

decreasing estimate of q across the sequence of models from OE to PE0.1, from 0.0741 to

0.0387. As predicted indices more closely match observed indices, the difficulty in balancing the

aforementioned scenario of high full recruits following low recruitment minus substantial harvest

in the previous year is intensified. In order for the model to account for the unusually high

survival between years in this circumstance, the model minimizes the relative contribution of

harvest removals by amplifying stock size (i.e. decreasing q) in order to best fit the observed full

recruit index and minimize the residual.

The mixed error PE0.1 model was chosen as the preferred model configuration, given

the best fit to the observed survey indices. Higher priority was given to fitting the observed

indices in lieu of minimizing process error, given the high degree of confidence in the survey

indices as measures of relative stock abundance (Kahn et al. 1998). As discussed above,

reducing the influence of the model equation in the prediction of observed indices was helpful

given the aforementioned model equation difficulties in rectifying very low recruit index values

preceding relatively high full recruit indices. Consequently, assigning less weight to process

error residuals across the mixed error models reduced the influence of the model difference

equation, achieving a tighter fit to the observed data. Although no process error was generated

- 41 -

in the OE model, the sole predicted full recruit index was calculated entirely from the model

difference equation, which explains why the OE model provided the poorest fit the observed

indices. This approach in selecting the preferred model assumes that the survey indices contain

less error than the difference equation (Eq. 6). The remainder of the report presents results

from this model (PE0.1).

Combined-Sex Model

Model Outputs

Estimates of total, annual blue crab abundance from model years 1978 to 2008 ranged

from 29 to 614 million, with a mean and median of 155 and 135 million (Table 8; Figure 14).

Most of the fluctuation is caused by large annual variability in recruit numbers. Estimates of

annual recruit abundance ranged from 15 to 544 million across the assessment time period, with

a mean and median of 124 and 95 million recruits (Figure 15). Terminal year recruitment in

2008 was 35 million, the fifth lowest estimate since 1978. Full recruit abundance ranged

between 9 and 70 million crabs, with a mean and median of 31 million individuals (Figure 16). In

the earliest years of the assessment from 1978 to 1987 full-recruit abundance was low, falling

below the median in 9 of 10 years. Full-recruit abundance then stayed at or above the median

for 14 straight years until 2001 (Figure 16). A 5 year decline occurred from 1999 until 2003,

followed by a two-year increase in 2004-2005. Full-recruit abundance dropped to the second

lowest value in the assessment time series at 10 million crabs in 2006, punctuating a prolonged

5 year period of below-median low abundance. A temporary spike in full recruit abundance

occurred in 2007 to 37 million crabs followed by another low abundance value of 23 million in the

terminal year of 2008. Full recruit biomass ranged from 1.4 to 9.7 million kg, with a mean and

- 42 -

median of 4.4 and 4.2 million kg (Figure 17). Terminal year 2008 full-recruit biomass was 3.2

million kg.

Model CVs of estimated recruit and full recruit parameters were between 23.9% and

27.2%. The CV associated with the estimate of the catchability coefficient q improves with each

additional year of data; from 40.4% in 2005, 33.0% in 2007, and 30.9% in 2008. Terminal year

estimate of q was 0.0387, an increase from the prior estimate of 0.0371 in 2007, 0.0365 in 2006

and 0.0329 in 2005. Bootstrap CVs of annual recruit abundance ranged from 15.7% to 30.9%.

Full-recruit abundance bootstrap CVs ranged from 17.1% to 33.8%. The bootstrap CVs for Z

ranged from 12.4% to 44.8%. The bootstrap CV for the estimate of q was 14.4%. Bootstrap

means of all estimated parameters and output results are shown in the final NFT model output

report (see Appendix I).

Mortality Rates

Instantaneous total mortality rates (Z) across the assessment time series were variable

ranging between 0.50 and 2.66, with an average and median of 1.52 and 1.47 (Table 8; Figure

18). Terminal Z was 2.00, continuing a trend of at- or above-median Z since 1997. Average

annual survival rate (1-A) was 25.2% and ranged from 7.0 to 60.5 % across the time series.

Total mortality appears to be strongly, positively related to recruit abundance (Figure 19).

Exploitation rates are widely variable given the range in annual exploitable stock sizes

(Figure 20). The upper bound and Collie-Kruse estimates of exploitable stock size were most

variable due to dramatic fluxes in recruit abundance, whereas the lower bound estimates which

do not use prior year recruit abundance in calculating exploitable stock were fairly stable across

- 43 -

the time series. The lower bound, Collie-Kruse, and upper bound exploitation rates averaged

15%, 27%, and 38% over the 1978 to 2007 period (Table 8; Figure 21). Terminal year

exploitation rates (LB 15%, CK 28%, UB 53%) were above time series norms.

Estimates of fishing mortality rate rose in terminal model year 2007 well above time

series norms. The range of upper bound Fs were between 0.23 in 1978 and 1.79 in 2005,

averaging 0.78 across the time series with terminal UBF=1.22 (Table 8). The lower bound F

ranged between 0.08 in 1980 and 0.58 in 2005 averaging F =0.28 with terminal LBF=0.35 (Table

8). The Collie-Kruse F was generally between the upper and lower bound estimates except

when it exceeded the upper bound in 1982, 1983, 1987, 1988, 1990, and 1991 (Figure 22). The

Collie-Kruse and lower bound estimates of fishing mortality fluctuate similarly (Figure 22). Peak

Collie-Kruse F occurred in 2005 at F =1.05; the time series average was 0.51; terminal

CKF=0.64. Annual F calculated from Z – M was highly erratic, achieving implausible negative

values four times in the time series (Table 8). The average F from the Z-M method was F =0.70.

Indices of Relative Abundance

Young-of-the-year abundance as measured by survey CPT was depressed in 2000,

2002, and 2008, with a large spike in 2006 (Figure 23). Terminal 2008 YOY abundance is

among the lowest of the 31 year survey period. Survey CPT of medium-size crabs, large crabs,

spawning stock, and female spawning stock biomass in 2008 were similar to the previous year

values, reflecting the continued presence of a strong 2006 year class.

- 44 -

A general period of high productivity (i.e. elevated YOY abundance) appears to have

occurred for about 15 years from 1985 to 1999. As a result, indices of medium, large crabs, and

spawning stock were at or above the median in 13 of 17 years between 1986 and 2002 (Figures

24, 25, 26). A particularly weak YOY class in 2002 precipitated a four year period of low

abundance of mediums, large crabs, and spawning stock from 2003 to 2006. Since bottoming in

2003, medium crabs and spawning stock indices increased steadily until surpassing median

CPT values in 2007. The large crab index remains below the time series median in 2008

(Figure 25). The ISSB fell below the reduced recruitment threshold in 2003 and 2005 and has

increased to robust levels in 2006, 2007, 2008 (Figure 27).

Typically, high YOY abundance is a good forecast for improved medium abundance in

ensuing years (Figure 28). The relationship with future large crabs and SSB is not as strong due

to effects of harvest and other mortality factors after the recruit stage (Figures 29, 30).

Index-Based Stock Recruitment Model

The compensatory relationship between the indices of spawning biomass (t) and recruits

(t+1) produced a fit to a Ricker stock-recruitment model (Figure 31), with the resulting model

from nonlinear least squares being

R = 270.366 * SSB * exp(-45.904 * SSB),

where R = the index of recruits and SSB = the index of SSB. The index-based reference point

SSB50 was 0.005 kg/tow. Observed SSB in 2008 of 0.022 kg/tow should produce the maximum

predicted recruitment in 2009 based on the S-R model (Figure 31). The Ricker model is

- 45 -

consistent with the documented presence of cannibalism among blue crabs, which could provide

a mechanism for the depensatory recruitment pattern at large stock sizes.

DISCUSSION

Results from this assessment support the documented view of density dependent

mortality occurring on the Delaware Bay blue crab stock (Kahn et al. 1998; Helser and Kahn

1999; Kahn and Helser 2005). The most prominent error residuals followed a predictable

pattern reflective of high compensatory mortality following large recruitment events. This

explains why heavy recruitment into the fishery-sized adult population is not observed in the full

recruit index after especially large year-classes appear, while high survival to full recruitment is

observed following low pre-recruit levels. The inability to quantify a priori, year-specific natural

mortality rates to account for density dependent compensation in the model equation is

problematic in simulating stock dynamics based closely on the observed indices. Given

constant annual input M, the model cannot account for the disappearance of large numbers of

recruits necessary to fit the following year‟s full-recruit (adult) survey. This is increasingly evident

in residuals from models with higher weighting of process error and in the OE model, since

greater weight is given to the model-calculated full recruit index that is derived from a constant

M. The updated stock-recruit model also supports the view of density dependent mortality, as

the best fit to empirical data results in a Ricker S-R curve. Previous analyses of survey data also

indicated that recruits exhibited density-dependent mortality (Kahn et al. 1998 and updated in

Kahn 2003).

Model derived total mortality Z is an increasing function of recruit abundance. Given the

estimation of Fµ from a calculated exploitation rate (using known yearly catch, estimated stock

- 46 -

size, Z, and annual mortality rate), a secondary estimate of M can be calculated derived from Z -

Fµ. This year-specific M is strongly related to recruit abundance and explains much of the yearly

variation in Z (Figure 32). Although this post-hoc method of calculating M is partially conditional

on the original constant M input, it provides an ostensibly realistic estimate of time-varying M that

accounts for density dependent effects of recruit abundance. Cannibalism is likely the primary

mechanism that incurs greater natural mortality with increasing recruit densities. Predation

experiments show increased cannibalism by large blue crabs on small juveniles as juvenile

densities increased, demonstrating a strong propensity for density dependent regulation of

recruits (Peery 1989).

Stock status is assessed based on comparisons of F to an overfishing threshold, Frep

=1.3, and to yield-based reference points, Fmax =1.0 and F0.1 =0.6. The post-hoc calculations of

annual exploitable stock size from the model outputs directly affect the F rates used to assess

the stock. The estimation of exploitable stock size is uncertain due to the difficulty in discerning

the proportion of pre-recruits that grow into the full-recruit stage within the one year time step.

Kahn et al. (1998) documented rapid growth of juveniles, with recruitment into the harvestable

size range occurring by June, and peak recruitment into the legal size fishery in August-

September. Previous assessments assumed a partial recruitment =0.4 to account for fast

growing recruits (Helser and Kahn 1999; Coakley 2004). However, within-year recruitment is

difficult to quantify given the density dependent mortality and variable growth from year to year.

Instead, the use of upper and lower bounds of exploitable stock size in this assessment are

used to account for partial, within-year recruitment as in Kahn and Helser (2005). The upper

and lower range of F rates result from the lower and upper estimates of exploitable stock size.

The range of F rates used for management purposes was taken from a preferred model

- 47 -

choice (PE0.1) after an analysis of four error-weighting model configurations. These four

configurations differed in part by how well the observed survey indices were fit, the greater fit to

indices occurring with greater downweighting of process error residuals. Thus the mixed error

PE0.1 model was preferred because of its best fit to the observed data. A consequence to the

increasing fit to indices was the decline in the estimated q parameter. This resulted in

increasing estimates of abundance in those models, which consequently had a reciprocal,

diminishing effect on F calculations – in turn resulting in the lowest F rates produced by the

various error-weighted models.

Stock Status

Terminal estimates of F increased from the previous year. In 2005, high estimates of F

(e.g. FC-K=1.05) were observed, raising concern for a rising trend in F rates. A sharp reduction in

F occurred in 2006 to FC-K=0.44, while terminal FC-K rose to 0.64. The three-year mean FC-

K=0.71 is considerably higher than the 31 year median FC-K=0.48, yet below Fmax.

Viewing the UB F as a precautionary F indicator, the 30 year mean and median UB F lies

roughly between F0.1 and Fmax across all four error-weighting model configurations (Figure 33).

Mean UB F from the preferred model was 0.78, below the common F = M paradigm. F = M is

sometimes recommended as a surrogate for FMSY (Quinn & Deriso 1999). Deriso (1982) found

that M could be viewed as an upper bound for FMSY. Thompson (1993) found that a fishing

mortality under 80% of M should keep spawning biomass per recruit above 30% SPR. The 30

year mean FC-K=0.51 was equal to 64% of M (Figure 33). Over the most-recent 3 years, C-K F

averaged 0.71, above F0.1 and 0.8*M, and UB F averaged above Fmax at 1.23 (Figure 34).

- 48 -

Since bottoming in 2003, medium crab and spawning stock CPTs have gradually

improved until finally surpassing time series norms in 2007 and 2008. Depressed indices of

mediums, large crabs, and spawning stock were below-median for four years from 2003-2006.

This stock decline began with the very low 2002 YOY index, despite an extremely high 2002

spawning stock index. An unusually warm spring could have artificially spurred this high 2002

spawning stock CPT value. Regardless, this early warming period likely accelerated the timing

of spawning, as indicated by an early presence of sponge crabs in the survey in April and May,

and a shortened May sook run in the fishery (since females were gravid and unharvestable).

Earlier than usual spawning may have had negative implications on larval transport back into

estuarine nursery areas in Delaware Bay by interrupting the coordinated timing of larval

development and fall weather events (Epifanio 1995; Garvine et al. 1997; Nantunewicz et al.

2001). Thus weak larval recruitment in 2002 could be responsible for the very low YOY

abundance in the survey. Following the depressed YOY recruitment in August-October 2002,

severe mortality associated with very low winter temperatures likely occurred in January-March

2003, leading to a further decline in abundance (personal communication, D. Kahn). Low

dredge harvest is often an indicator of abnormally high winter mortality caused by unusually low

winter temperatures. Delaware dredge harvest was approximately 50% below-average in

January-March 2003. The combination of low YOY recruitment in 2002 followed by elevated

winter mortality in 2003 would reduce population size considerably, as seen in the zero CPT in

the 2003 ISSB. Continued low YOY recruitment in 2003 would be expected following the zero

2003 ISSB. This low population abundance was seen in the depressed fishery landings in 2003

and 2004. Landings in 2003 and 2004 in Delaware were 72% of the 1973-2006 average. A

healthy rebound in harvest in 2005 and 2006 during persistently low levels of recruitment and

abundance explains the abnormally high 2005-2006 F rate from the population model. The

- 49 -

elevated landings since 2005 probably prolonged the recovery period. The only index the

remains below the median is the large crab index. Large crabs may be the last to respond as

the stock initially recovers due to the heavy harvest of jimmies (largest males) in the fishery.

The index of spawning stock biomass has shown small incremental increases since

2003, persisting at or above the SSB50 threshold since 2004. Kahn (2003) refers to the SSB50

as the reduced recruitment threshold, indicating that as the ISSB falls below SSB50, the

likelihood of low observed recruitment increases. Median recruitment is 0.77 CPT when the

ISSB is below the SSB50 threshold compared to 1.45 CPT at ISSB values above SSB50. Based

on the S-R curve, the 2008 ISSB should result in the maximum theoretical recruitment event in

2009.

This work portrays a highly resilient stock under substantial exploitation pressure.

Terminal year young-of-the-year abundance in 2008 is among the worst in 31 years, yet standing

spawning stock biomass should yield high juvenile recruitment in 2009. Fishing mortality rates

across the most-recent three years are well above time series norms, yet below Fmax. Stock

status in the terminal year in terms of abundance and F is below-average, yet these metrics

should rebound in the near future given expected recovery in recruitment.

ACKNOWLEDGMENTS

Much gratitude is given to Lindy Barry, Tom Baum, Jeffrey Brust, Brandon Muffley, and

Paul Scarlett of NJ Bureau of Marine Fisheries, and Bill Whitmore and Rick Cole of DE Division

of Fish and Wildlife for historical NJ and DE landings statistics. Further acknowledgment is

given to Dr. Desmond Kahn of DE DFW for both his quantitative and anecdotal contributions to

- 50 -

this report. Funding for this research was provided by NOAA under the Atlantic Coastal

Fisheries Cooperative Management Act (ACFMA).

- 51 -

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TABLES

Table 1. Annual (Jan-Dec) combined commercial and recreational landings (kg) by state (1973-2008).

Year Delaware New Jersey Total Landings

DE% NJ%

1973 659,911 820,173 1,480,085

44.6% 55.4%

1974 833,411 987,466 1,820,877

45.8% 54.2%

1975 1,423,009 956,288 2,379,297

59.8% 40.2%

1976 1,404,644 877,861 2,282,506

61.5% 38.5%

1977 317,301 118,850 436,151

72.8% 27.2%

1978 135,747 335,654 471,402

28.8% 71.2%

1979 225,815 315,225 541,041

41.7% 58.3%

1980 786,461 610,516 1,396,977

56.3% 43.7%

1981 373,715 572,024 945,739

39.5% 60.5%

1982 384,735 291,567 676,303

56.9% 43.1%

1983 468,405 495,956 964,361

48.6% 51.4%

1984 449,456 664,928 1,114,384

40.3% 59.7%

1985 1,132,213 1,019,033 2,151,246

52.6% 47.4%

1986 1,272,152 1,088,662 2,360,813

53.9% 46.1%

1987 1,594,431 1,108,155 2,702,585

59.0% 41.0%

1988 1,631,292 1,538,426 3,169,719

51.5% 48.5%

1989 2,156,766 1,577,485 3,734,251

57.8% 42.2%

1990 3,042,722 1,609,572 4,652,295

65.4% 34.6%

1991 2,323,051 1,498,659 3,821,710

60.8% 39.2%

1992 2,102,506 2,008,828 4,111,334

51.1% 48.9%

1993 2,769,425 2,386,022 5,155,447

53.7% 46.3%

1994 2,578,601 1,747,332 4,325,933

59.6% 40.4%

1995 2,953,825 2,794,578 5,748,403

51.4% 48.6%

1996 2,025,045 1,066,922 3,091,967

65.5% 34.5%

1997 2,123,682 1,327,959 3,451,641

61.5% 38.5%

1998 2,152,935 2,089,433 4,242,368

50.7% 49.3%

1999 2,320,158 2,064,485 4,384,643

52.9% 47.1%

2000 1,942,930 1,790,908 3,733,838

52.0% 48.0%

2001 1,765,894 1,925,687 3,691,581

47.8% 52.2%

2002 1,468,479 2,087,797 3,556,275

41.3% 58.7%

2003 712,223 973,332 1,685,555

42.3% 57.7%

2004 1,141,669 1,148,463 2,290,132

49.9% 50.1%

2005 1,460,426 2,070,484 3,530,910

41.4% 58.6%

2006 1,495,913 1,808,890 3,304,803

45.3% 54.7%

2007 1,785,263 1,720,550 3,505,813

50.9% 49.1%

2008 1,885,928 2,212,242 4,098,170

46.0% 54.0%

Average 1,480,559 1,325,289 2,805,849

51.7% 48.3%

- 62 -

Table 2. Historic, annual, Delaware Bay blue crab landings in Delaware by fishery and market grade based on a calendar year (Jan-Dec). Landings are shown in thousands of kilograms.

Commercial Dredge Commercial Pot Recreational

Total Year 1 2 3 1 2 3 Peeler Hard Crabs

1973 0 0.0 0 245 169 222 8 16 660

1974 5 0.0 26 298 317 126 44 19 833

1975 20 0.3 148 447 282 475 20 30 1,423

1976 53 0.2 203 336 320 415 50 27 1,405

1977 123 0.0 12 90 32 50 6 4 317

1978 0 0.0 0 49 41 35 7 3 136

1979 2 0.0 17 71 52 71 9 5 226

1980 7 0.0 60 190 105 394 13 17 786

1981 1 0.0 7 148 101 82 25 8 374

1982 5 0.0 27 167 58 113 6 8 385

1983 1 0.0 11 170 54 216 5 11 468

1984 4 0.0 38 170 100 111 17 10 449

1985 8 0.0 70 485 248 279 17 25 1,132

1986 19 0.0 197 266 372 348 47 25 1,272

1987 17 0.0 302 347 419 451 28 30 1,594

1988 30 0.2 361 239 474 429 71 29 1,631

1989 20 0.0 367 491 399 785 53 42 2,157

1990 46 0.0 481 991 753 624 88 59 3,043

1991 29 0.0 207 733 249 1,043 11 51 2,323

1992 9 0.0 144 420 798 488 200 43 2,103

1993 38 0.0 547 706 473 869 86 51 2,769

1994 22 0.0 502 670 591 608 138 47 2,579

1995 5 0.0 256 1,017 636 745 235 60 2,954

1996 47 0.0 623 427 405 392 100 31 2,025

1997 35 0.0 336 554 329 780 49 42 2,124

1998 24 0.0 254 661 537 543 91 44 2,153

1999 22 0.0 308 835 552 512 43 47 2,320

2000 23 0.0 283 841 283 438 35 39 1,943

2001 17 0.0 379 828 191 292 26 33 1,766

2002 27 0.0 221 613 175 386 16 29 1,468

2003 15 0.0 137 313 82 135 8 23 712

2004 22 2.1 91 615 114 220 38 41 1,142

2005 17 0.3 97 686 331 236 40 54 1,460

2006 21 0.0 179 588 247 389 20 53 1,496

2007 34 0.1 226 648 340 441 35 62 1,785

2008 33 0.0 247 556 344 618 22 66 1,886

Average 22 0 204 470 305 399 47 33 1,481

- 63 -

Table 3. Historical, annual, Delaware Bay blue crab landings in New Jersey by fishery and market grade

based on a calendar year. Landings are shown in thousands of kilograms.

Commercial Dredge Commercial Pot

Recreational Total

Harvest Year Female Male Mixed Female Male Mixed Peeler Mixed

1950 - - 110 - - 392 5 76 583

1951 - - 70 - - 161 4 31 266

1952 - - 48 - - 217 3 42 310

1953 - - 8 - - 162 2 31 203

1954 - - 3 - - 252 3 49 306

1955 - - 24 - - 140 4 27 195

1956 - - 35 - - 138 3 27 202

1957 - - 29 - - 309 2 60 400

1958 - - 48 - - 165 2 32 246

1959 - - 51 - - 197 0 38 286

1960 - - 63 - - 341 6 66 477

1961 - - 24 - - 148 21 29 221

1962 - - 40 - - 382 56 74 552

1963 - - 20 - - 225 12 44 300

1964 - - 11 - - 153 3 30 197

1965 - - 26 - - 227 12 44 308

1966 - - 17 - - 177 1 34 229

1967 - - 7 - - 129 2 25 163

1968 - - 3 - - 35 0 7 45

1969 - - 2 - - 188 3 36 230

1970 - - 0 - - 232 12 45 289

1971 - - 7 - - 326 5 63 401

1972 - - 27 - - 387 5 75 494

1973 - - 94 - - 601 8 116 820

1974 - - 47 - - 750 45 145 987

1975 - - 80 - - 722 14 140 956

1976 - - 102 - - 623 33 121 878

1977 - - 18 - - 83 2 16 119

1978 - - 2 - - 274 7 53 336

1979 - - 8 - - 250 10 48 315

1980 - - 62 - - 455 6 88 611

1981 - - 9 - - 457 17 88 572

1982 - - 0 - - 242 4 45 292

1983 - - 0 - - 409 8 79 496

1984 - - 2 - - 555 13 95 665

1985 - - 31 - - 838 45 104 1,019

1986 - - 104 - - 793 40 154 1,093

1987 - - 245 - - 696 33 134 1,109

1988 - - 223 - - 1,006 106 204 1,539

1989 - - 221 - - 1,068 75 213 1,577

- 64 -

1990 - - 131 - - 1,126 133 219 1,610

1991 - - 86 - - 1,166 17 229 1,499

1992 - - 57 - - 1,505 148 299 2,009

1993 - - 333 - - 1,649 69 335 2,387

1994 - - 100 - - 1,246 155 251 1,752

1995 - - 187 - - 1,887 346 374 2,795

1996 - - 133 - - 721 65 147 1,067

1997 - - 58 - - 979 92 199 1,328

1998 - - 102 - - 1,525 173 290 2,089

1999 - - 14 - - 1,614 121 315 2,064

2000 - - 44 - - 1,401 70 276 1,791

2001 133 11 0 417 973 24 88 280 1,926

2002 100 4 0 503 1,070 24 94 292 2,087

2003 57 11 0 136 570 12 45 143 973

2004 72 11 0 129 690 5 76 165 1,148

2005 67 15 2 293 1,249 11 129 304 2,070

2006 52 5 0 445 968 9 66 263 1,808

2007 32 3 0 415 884 12 116 259 1,720

2008 23 2 0 541 1,206 7 85 347 2,212

Average 67 8 54 360 951 506 46 132 926

- 65 -

Table 4. Annual commercial fishing licenses sold by state. New Jersey dredge fishery licenses from 1990-

1996 included all state waterbodies. From 1997 on, totals indicate Delaware Bay dredge licenses only.

Delaware Commercial Licenses New Jersey Commercial Licenses

Season Crab Pot Dredge Total %

Change Crab Pot Dredge Total

%

Change

1975 91 12 103 - - - - -

1976 106 22 128 24% - - - -

1977 66 26 92 -28% - - - -

1978 40 0 40 -57% - - - -

1979 45 0 45 13% - - - -

1980 67 10 77 71% - - - -

1981 56 0 56 -27% - - - -

1982 53 5 58 4% - - - -

1983 60 5 65 12% - - - -

1984 70 5 75 15% - - - -

1985 77 6 83 11% - - - -

1986 102 12 114 37% - - - -

1987 111 15 126 11% - - - -

1988 126 5 131 4% - - - -

1989 132 22 154 18% - - - -

1990 172 31 203 32% 311 166 477 -

1991 169 16 185 -9% 312 133 445 -7%

1992 164 30 194 5% 365 209 574 29%

1993 184 23 207 7% 420 289 709 24%

1994 219 42 261 26% 506 222 728 3%

1995 219 42 261 0% 458 280 738 1%

1996 219 40 259 -1% 430 301 731 -1%

1997 214 40 254 -2% 408 93 501 -

1998 214 17 231 -9% 394 82 476 -5%

1999 214 37 251 9% 377 81 458 -4%

2000 212 35 247 -2% 364 90 454 -1%

2001 212 34 246 0% 352 91 443 -2%

2002 209 34 243 -1% 346 80 426 -4%

2003 204 33 237 -2% 333 94 427 0%

2004 204 38 242 2% 325 92 417 -2%

2005 204 36 240 -1% 319 93 412 -1%

2006 202 35 237 -1% 314 86 400 -3%

2007 218 36 254 7% 309 87 396 -1%

2008 206 39 245 -4% 302 86 388 -2%

- 66 -

Market GradeLandings

Unit

Common Unit

Equivalent

Numbers per

Landings Unit

#1 Male Hard Crab; pot bushel 40 lb 93.8

#1 Male Hard Crab; dredge bushel 40 lb 114.0

#2 Male Hard Crab; (both gears) bushel 40 lb 134.7

#3 Female Hard Crab; (both gears) bushel 40 lb 123.0

Hard Crab (unspecified male); dredge bushel 40 lb 114.492

Hard Crab (unspecified male); pot bushel 40 lb 110.477

Hard Crab (unspecified); dredge bushel 40 lb 122.322

Hard Crab (unspecified); pot bushel 40 lb 114.844

Hard Crab (unspecified); pot; Apr bushel 40 lb 118.277

Hard Crab (unspecified); pot; May bushel 40 lb 117.673

Hard Crab (unspecified); pot; Jun bushel 40 lb 114.479

Hard Crab (unspecified); pot; Jul bushel 40 lb 114.990

Hard Crab (unspecified); pot; Aug bushel 40 lb 113.391

Hard Crab (unspecified); pot; Sep bushel 40 lb 114.076

Hard Crab (unspecified); pot; Oct bushel 40 lb 114.504

Hard Crab (unspecified); pot; Nov bushel 40 lb 114.097

Peeler bushel 62.49 lb 300

Peeler pound - 4.801*

Peeler numbers 0.2083 lb* -

Table 5. Bushels to numbers conversions used in the assessment.

- 67 -

Table 6. Inputs used in the CSA model for the baseline combined-sex model.

Survey Indices (#/tow) Survey Avg. Wt. (kg) Harvest

Survey

Year Recruits

Full

Recruits Recruits Full Recruits Numbers x 10

6 kg / individual

1978 2.179413968 0.350253368 0.015 0.157 3.26 0.1545

1979 1.32930109 0.774146407 0.022 0.144 7.27 0.1545

1980 5.767955596 0.468614581 0.010 0.171 6.58 0.1526

1981 2.030260442 1.513766476 0.015 0.144 4.48 0.1597

1982 0.544536843 0.46892669 0.028 0.154 5.87 0.1570

1983 0.883959568 0.546902374 0.011 0.176 5.72 0.1562

1984 3.361388811 0.964780884 0.008 0.168 11.00 0.1556

1985 7.966658785 0.608828139 0.003 0.169 17.14 0.1523

1986 1.56224118 0.862671413 0.013 0.137 18.03 0.1514

1987 2.935679713 0.743670955 0.003 0.139 18.31 0.1481

1988 3.861174428 1.508443138 0.007 0.140 25.73 0.1494

1989 24.96839025 2.898483119 0.006 0.138 28.29 0.1504

1990 0.738158815 1.064904509 0.009 0.167 24.71 0.1584

1991 4.7393749 1.317453373 0.005 0.200 26.76 0.1458

1992 3.737739177 2.492882919 0.012 0.139 33.85 0.1525

1993 8.174420139 1.453676758 0.003 0.157 30.09 0.1496

1994 11.21657274 1.392456331 0.001 0.144 36.44 0.1455

1995 2.640472671 1.458674286 0.002 0.132 24.81 0.1528

1996 4.199889055 1.227599426 0.004 0.132 23.34 0.1512

1997 14.50449176 1.506677451 0.005 0.131 25.85 0.1497

1998 5.31589812 1.590245527 0.010 0.133 29.74 0.1544

1999 9.411201926 1.545717644 0.005 0.136 25.10 0.1567

2000 8.346600638 1.415226221 0.005 0.126 23.48 0.1578

2001 3.543692105 1.016729103 0.009 0.145 24.94 0.1570

2002 2.555592295 0.717219467 0.007 0.143 11.63 0.1576

2003 3.774410082 0.645217539 0.006 0.150 14.10 0.1588

2004 4.337943308 0.83509377 0.006 0.162 18.69 0.1574

2005 3.305993672 1.209721485 0.006 0.147 23.91 0.1580

2006 5.944976484 0.367942464 0.004 0.135 20.32 0.1552

2007 5.767057689 1.423435108 0.005 0.133 26.42 0.1560

2008 1.363581233 0.831014775 0.013 0.134

Mean 5.19 1.14 0.008 0.148 19.86 0.1539

2 y Mean 3.57 1.13 0.009 0.134 23.37 0.1556

- 68 -

Index of Abundance Units Survey Period Size Subset

YOY Index GM CPT (numbers) Sep-Oct < 60 mm

Recruit Index GM CPT (numbers) Apr-Aug 60 - 119 mm

Index of Large Crabs GM CPT (numbers) Apr-Oct >= 120 mm

Index of Spawning Stock AM CPT (numbers) Apr-May >= 120 mm

Index of Spawning Stock Biomass AM CPT (kg) Apr-May females >= 120 mm

Table 7. Supplementary fishery independent indices of population abundance from the DDFW trawl survey.

- 69 -

Table 8. Baseline combined-sex model outputs and calculated quantities from the preferred model PE0.1.

Model Results q = 0.03868

Upper B C-K Lower B Lower B C-K Upper B Lower B C-K Upper B Z-M upper B C-K Lower B

Survey Year RecruitsPost-Recruits Total Harvest Z A stock size stock size stock size U U U F F F F M M M

1978 54.98 9.02 64.00 3.26 1.16 0.68 64.0 35.1 23.4 0.05 0.09 0.14 0.086 0.16 0.23 0.36 1.07 1.00 0.92

1979 33.33 20.16 53.49 7.27 1.45 0.77 53.5 29.4 19.8 0.14 0.25 0.37 0.258 0.47 0.70 0.65 1.20 0.98 0.76

1980 142.00 12.51 154.51 6.58 1.37 0.75 154.5 84.8 45.8 0.04 0.08 0.14 0.078 0.14 0.26 0.57 1.29 1.23 1.11

1981 49.49 39.23 88.71 4.48 1.85 0.84 88.7 48.7 18.4 0.05 0.09 0.24 0.111 0.20 0.54 1.05 1.74 1.65 1.32

1982 14.71 13.91 28.62 5.87 0.73 0.52 28.6 15.7 19.7 0.21 0.37 0.30 0.289 0.53 0.42 -0.07 0.44 0.20 0.31

1983 24.12 13.82 37.94 5.72 0.50 0.40 37.9 20.8 28.7 0.15 0.27 0.20 0.192 0.35 0.25 -0.30 0.31 0.15 0.25

1984 80.45 22.94 103.39 11.00 1.81 0.84 103.4 56.7 27.9 0.11 0.19 0.39 0.231 0.42 0.86 1.01 1.58 1.39 0.96

1985 182.84 16.86 199.70 17.14 2.07 0.87 199.7 109.6 42.4 0.09 0.16 0.40 0.203 0.37 0.96 1.27 1.86 1.70 1.11

1986 41.48 25.29 66.77 18.03 1.26 0.72 66.8 36.6 37.0 0.27 0.49 0.49 0.475 0.86 0.86 0.46 0.78 0.39 0.40

1987 78.64 18.97 97.61 18.31 0.93 0.60 97.6 53.6 56.9 0.19 0.34 0.32 0.288 0.52 0.49 0.13 0.64 0.40 0.43

1988 105.09 38.60 143.69 25.73 0.72 0.51 143.7 78.9 95.6 0.18 0.33 0.27 0.251 0.46 0.38 -0.08 0.47 0.26 0.34

1989 543.74 69.90 613.64 28.29 2.66 0.93 613.6 336.8 71.2 0.05 0.08 0.40 0.132 0.24 1.14 1.86 2.53 2.42 1.52

1990 21.86 42.92 64.78 24.71 0.76 0.53 64.8 35.6 55.0 0.38 0.69 0.45 0.544 0.99 0.64 -0.04 0.21 -0.23 0.12

1991 126.18 30.33 156.51 26.76 0.92 0.60 156.5 85.9 89.0 0.17 0.31 0.30 0.262 0.48 0.46 0.12 0.66 0.44 0.46

1992 95.30 62.28 157.58 33.85 1.44 0.76 157.6 86.5 71.4 0.21 0.39 0.47 0.405 0.74 0.89 0.64 1.03 0.70 0.54

1993 194.88 37.51 232.39 30.09 1.81 0.84 232.4 127.5 68.3 0.13 0.24 0.44 0.280 0.51 0.95 1.01 1.53 1.30 0.85

1994 261.39 38.17 299.56 36.44 1.98 0.86 299.6 164.4 78.0 0.12 0.22 0.47 0.279 0.51 1.07 1.18 1.70 1.47 0.90

1995 68.77 41.55 110.32 24.81 1.26 0.72 110.3 60.5 56.2 0.22 0.41 0.44 0.395 0.72 0.78 0.46 0.86 0.54 0.48

1996 107.28 31.40 138.68 23.34 1.27 0.72 138.7 76.1 62.2 0.17 0.31 0.38 0.298 0.54 0.66 0.47 0.98 0.73 0.61

1997 332.83 38.82 371.65 25.85 2.10 0.88 371.7 204.0 71.5 0.07 0.13 0.36 0.166 0.30 0.86 1.30 1.93 1.79 1.23

1998 132.80 45.63 178.44 29.74 1.48 0.77 178.4 97.9 70.3 0.17 0.30 0.42 0.320 0.58 0.81 0.68 1.16 0.90 0.67

1999 221.65 40.56 262.21 25.10 1.90 0.85 262.2 143.9 64.3 0.10 0.17 0.39 0.214 0.39 0.87 1.10 1.69 1.51 1.03

2000 193.13 39.18 232.31 23.48 2.09 0.88 232.3 127.5 52.2 0.10 0.18 0.45 0.241 0.44 1.07 1.29 1.85 1.65 1.02

2001 86.23 28.72 114.95 24.94 1.79 0.83 114.9 63.1 44.1 0.22 0.40 0.57 0.466 0.85 1.21 0.99 1.32 0.94 0.58

2002 62.99 19.19 82.18 11.63 1.56 0.79 82.2 45.1 28.9 0.14 0.26 0.40 0.279 0.51 0.79 0.76 1.28 1.05 0.77

2003 92.21 17.28 109.50 14.10 1.58 0.79 109.5 60.1 36.6 0.13 0.23 0.38 0.256 0.47 0.77 0.78 1.32 1.11 0.81

2004 107.94 22.54 130.48 18.69 1.44 0.76 130.5 71.6 49.5 0.14 0.26 0.38 0.271 0.49 0.71 0.64 1.17 0.95 0.73

2005 75.82 30.82 106.64 23.91 2.32 0.90 106.6 58.5 34.4 0.22 0.41 0.70 0.577 1.05 1.79 1.52 1.74 1.27 0.53

2006 146.83 10.47 157.31 20.32 1.44 0.76 157.3 86.3 57.5 0.13 0.24 0.35 0.244 0.44 0.67 0.64 1.20 1.00 0.77

2007 135.60 37.21 172.81 26.42 2.00 0.86 172.8 94.8 49.9 0.15 0.28 0.53 0.353 0.64 1.22 1.20 1.64 1.35 0.77

2008 35.25 23.44 58.69 58.7 32.2

mean 124.19 30.53 154.48 19.86 1.52 0.75 157.68 86.54 50.87 0.15 0.27 0.38 0.28 0.51 0.78 0.72 1.24 1.01 0.74

median 95.30 30.58 134.58 23.41 1.47 0.77 134.58 73.86 51.03 0.14 0.26 0.39 0.27 0.48 0.78 0.67 1.24 1.00 0.76

3 y mean 105.89 23.71 129.60 23.55 1.92 0.84 145.59 79.90 47.26 0.17 0.31 0.53 0.39 0.71 1.23 1.12 1.53 1.21 0.69

2 y mean 85.42 30.33 115.75 23.37 1.72 0.81 165.06 90.59 53.70 0.14 0.26 0.44 0.30 0.54 0.95 0.92 1.42 1.18 0.77

Min 14.71 9.02 28.62 3.26 0.50 0.40 28.62 15.71 18.39 0.04 0.08 0.14 0.08 0.14 0.23 -0.30 0.21 -0.23 0.12

Max 543.74 69.90 613.64 36.44 2.66 0.93 613.64 336.77 95.63 0.38 0.69 0.70 0.58 1.05 1.79 1.86 2.53 2.42 1.52

Stock Size (Millions) Sep 1

- 70 -

Figure 1. Delaware Bay blue crab size frequency distributions from research trawl survey.

0 20 40 60 80 100 120 140 160 180 200

1

10

100

1000

0 20 40 60 80 100 120 140 160 180 200

1

10

100

10000 20 40 60 80 100 120 140 160 180 200

1

10

100

1000

0 20 40 60 80 100 120 140 160 180 200

1

10

100

10000 20 40 60 80 100 120 140 160 180 200

1

10

100

1000

0 20 40 60 80 100 120 140 160 180 200

1

10

100

10000 20 40 60 80 100 120 140 160 180 200

1

10

100

1000

0 20 40 60 80 100 120 140 160 180 200

1

10

100

1000 Year=1979 Month=7

Year=1980 Month=5

Year=1980 Month=4

Year=1979 Month=8

Year=1979 Month=9

Year=1979 Month=10 Year=1980 Month=7

Year=1980 Month=6

Carapace Width (mm)

Log

10 F

requency

FIGURES

- 71 -

0 20 40 60 80 100 120 140 160 180 200

1

10

100

1000

0 20 40 60 80 100 120 140 160 180 200

1

10

100

1000

0 20 40 60 80 100 120 140 160 180 200

1

10

100

1000 0 20 40 60 80 100 120 140 160 180 200

1

10

100

1000 0 20 40 60 80 100 120 140 160 180 200

1

10

100

1000

0 20 40 60 80 100 120 140 160 180 200

1

10

100

10000 20 40 60 80 100 120 140 160 180 200

1

10

100

1000

0 20 40 60 80 100 120 140 160 180 200

1

10

100

1000

Year=1980 Month=8

Year=1980 Month=9

Year=1980 Month=10

Year=1981 Month=4

Year=1981 Month=5

Year=1981 Month=8

Year=1981 Month=7

Year=1981 Month=6

Carapace Width (mm)

Log

10 F

requency

Figure 1 (Continued).

- 72 -

Age (years)

0 1 2 3 4 5 6 7 8

Pred

icted

Car

apac

e W

idth

(mm

)

0

50

100

150

200

250

K=0.75 Lmax=234.7

K=0.62 Lmax=200.6

K=0.93 Lmax=200.3

Figure 2. Predicted growth trajectories derived from von Bertalanffy growth parameters estimatedby MULTIFAN applied to Delaware research trawl survey size frequency distributions.

0

50

100

150

200

250

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

Age (yr)

Ca

rap

ace

Wid

th (

mm

)

Female 1

Female 2

Male 1

Male 2

Figure 3. Male and female seasonal growth curves estimated using a modified ELEFAN method in the

LFDA analysis.

- 73 -

BLUE CRAB MATURATION BY WIDTH

Width (mm)

60 70 80 90 100 110 120 130 140 150 160 170 180 190

Pro

port

ion F

em

ale

s M

atu

re

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

ObservedPredicted

n = 3869

0

1

2

3

4

5

6

19

73

19

75

19

77

19

79

19

81

19

83

19

85

19

87

19

89

19

91

19

93

19

95

19

97

19

99

20

01

20

03

20

05

20

07

Har

vest

kg

Mil

lio

ns

Delaware

New Jersey

Figure 4. Observed and predicted proportion of maturity by carapace width for Delaware Bay female blue

crabs. Predicted maturity was estimated using logistic regression applied to data from unculled at-sea

samples from the Delaware commercial fishery, 1995-1997.

Figure 5. Annual combined commercial and recreational landings weight of Delaware Bay blue crabs by

state.

R2 = 0.97

- 74 -

0%

5%

10%

15%

20%

25%

1 2 3 4 5 6 7 8 9 10 11 12

Lan

din

gs

Month

sook run

0

5

10

15

20

25

19

73

19

75

19

77

19

79

19

81

19

83

19

85

19

87

19

89

19

91

19

93

19

95

19

97

19

99

20

01

20

03

20

05

20

07

Mil

lio

ns

Males Females

Figure 6. Monthly commercial blue crab landings in Delaware from 1973 to 2008 based on fishermen

submitted logbook records.

Figure 7. Annual male and female Delaware and New Jersey total landings in numbers.

- 75 -

0

500,000

1,000,000

1,500,000

2,000,000

2,500,000

3,000,000

3,500,000

1978 1980 1982 1984 1986 1988 1990 1992 1994 1996 1998 2000 2002 2004

Kilo

gra

ms

Logbooks Survey

_̂_̂_̂

_̂

_̂_̂

_̂_̂_̂

_̂̂_

_̂ _̂_̂_̂_̂̂_̂_

_̂_̂_̂_̂

_̂_̂_̂

_̂Maurice River

Mispillion River

Leipsic River

Delaware

New Jersey

_̂_̂̂_̂_̂_

_̂_̂

_̂

_̂_̂

_̂_̂_̂

_̂

_̂

_̂

26 Core Sites Used in Assessment

Supplemental Survey Sites

Figure 8. Annual DE landings calculated from the DDFW dockside intercept survey versus fishermen

submitted logbook reports.

Figure 9. Delaware

Division of Fish and

Wildlife Trawl Survey

stations.

- 76 -

0

10

20

30

40

50

60

1978

1980

1982

1984

1986

1988

1990

1992

1994

1996

1998

2000

2002

2004

Nu

mb

ers

(m

illi

on

s)

2004 Assessment

2004 (unexpanded NJ landings)

2005 Assessment

2006 Assessment

0

5

10

15

20

25

0 5 10 15 20 25

Model E

stim

ate

d R

ecru

its

Observed Recruits

Figure 10. Annual harvests calculated in 2004, 2005, and 2006 illustrating the effects of

methodological progressions in quantifying harvest.

Figure 11. Residual pattern of under-prediction of recruits in the assessment model as the

observed recruit index CPT increases.

- 77 -

-0.5

-0.4

-0.3

-0.2

-0.1

0.0

0.1

0.2

-0.20 -0.10 0.00 0.10 0.20

Fu

ll-R

ec

ruit

Re

sid

ua

ls y

+1

Recruit Residuals y

-0.7

-0.6

-0.5

-0.4

-0.3

-0.2

-0.1

0.0

0.1

0.2

0.3

0 5 10 15 20 25

Fu

ll R

ecru

it R

esid

uals

y+

1

Observed Recruits y

Figure 12. Residual pattern of over-prediction of full recruits in the year following high observed recruit

CPT.

Figure 13. Negative relationship between recruit residuals and full recruit residuals in the following year.

- 78 -

0

100

200

300

400

500

600

19

78

19

80

19

82

19

84

19

86

19

88

19

90

19

92

19

94

19

96

19

98

20

00

20

02

20

04

20

06

20

08

Mil

lio

ns

Recruits

Full Recruits

Harvest

0

100

200

300

400

500

600

Mil

lio

ns

Recruits

median

Figure 14. Preferred-model estimates of recruit and full recruit abundance in relation to observed harvest

in numbers.

Figure 15. Preferred-model estimates of annual recruit abundance in numbers.

- 79 -

0

10

20

30

40

50

60

70

80M

illio

ns

Post-Recruits

median

0

2

4

6

8

10

19

78

19

80

19

82

19

84

19

86

19

88

19

90

19

92

19

94

19

96

19

98

20

00

20

02

20

04

20

06

20

08

Mil

lio

ns

(k

g)

Full Recruit Biomass

Harvest

Median Harvest

Figure 16. Preferred-model estimates of annual full recruit abundance in numbers.

Figure 17. Preferred-model estimates of annual full recruit biomass (Sep 1) in relation to observed harvest

weight.

- 80 -

0.0

0.5

1.0

1.5

2.0

2.5

3.0

19

78

19

80

19

82

19

84

19

86

19

88

19

90

19

92

19

94

19

96

19

98

20

00

20

02

20

04

20

06

Ins

tan

tan

eo

us

To

tal M

ort

ali

ty R

ate

Z

Median

0.0

0.5

1.0

1.5

2.0

2.5

3.0

0 100 200 300 400 500 600

Ins

tan

tan

eo

us

To

tal M

ort

ali

ty R

ate

Z

Recruits x million

Figure 18. Estimates of annual instantaneous total mortality rate Z from the preferred-model PE0.1.

Figure 19. Estimates of Z shown as a function of annual recruit abundance from the preferred-model

PE0.1.

- 81 -

0

100

200

300

400

500

600

700

19

78

19

80

19

82

19

84

19

86

19

88

19

90

19

92

19

94

19

96

19

98

20

00

20

02

20

04

20

06

20

08

Exp

loit

ab

le S

tock (

nu

mb

ers

x m

illi

on

)

Upper B

C-K

Lower B

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

19

78

19

80

19

82

19

84

19

86

19

88

19

90

19

92

19

94

19

96

19

98

20

00

20

02

20

04

20

06

20

08

Exp

loit

ati

on

Rate

Upper Bound

Collie-Kruse

Lower Bound

Figure 20. Range of exploitable stock size estimates.

Figure 21. Range of annual exploitation rates.

- 82 -

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

19

78

19

80

19

82

19

84

19

86

19

88

19

90

19

92

19

94

19

96

19

98

20

00

20

02

20

04

20

06

20

08

Fis

hin

g M

ort

ali

ty F

Upper Bound F Collie-Kruse F Lower Bound F

Frep

F0.1

Fmax

Figure 22. Range of annual fishing mortality rates generated from the catch equation derived from three

estimates of exploitable stock size.

- 83 -

0.0

1.0

2.0

3.0

4.0

19

78

19

80

19

82

19

84

19

86

19

88

19

90

19

92

19

94

19

96

19

98

20

00

20

02

20

04

20

06

20

08

Geo

metr

ic M

ean

CP

T

Median

0

5

10

15

20

25

30

35

40

45

1978

1980

1982

1984

1986

1988

1990

1992

1994

1996

1998

2000

2002

2004

2006

2008

Geo

metr

ic M

ean

CP

T

Median

Figure 23. YOY index.

Figure 24. Index of Recruits (medium crabs).

- 84 -

0.0

0.4

0.8

1.2

1.6

19

78

19

80

19

82

19

84

19

86

19

88

19

90

19

92

19

94

19

96

19

98

20

00

20

02

20

04

20

06

20

08

Geo

metr

ic M

ean

CP

T Median

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

19

78

19

80

19

82

19

84

19

86

19

88

19

90

19

92

19

94

19

96

19

98

20

00

20

02

20

04

20

06

20

08

Ari

thm

eti

c M

ean

CP

T

Median

Figure 25. Index of Large Crabs.

Figure 26. Index of Spawners. Spawning stock is composed of males and females and expressed in

numbers.

- 85 -

0.00

0.02

0.04

0.06

0.08

0.10

0.12

0.14

1984

1986

1988

1990

1992

1994

1996

1998

2000

2002

2004

2006

2008

Ari

thm

eti

c M

ean

CP

T (kg

)Index of SSB

SSB50 Threshold

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

4.5

0 10 20 30 40 50

Recru

its (

y+

1)

YOY Index (y)

Figure 27. Index of Spawning Stock Biomass. Spawning stock biomass is composed of females only.

Figure 28. Relationship between YOY abundance and recruit abundance in the following year.

- 86 -

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

0 10 20 30 40 50

Larg

e C

rab

s (

y+

2)

YOY Index (y)

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0 10 20 30 40 50

Sp

aw

ners

(y+

2)

YOY Index (y)

Figure 29. Relationship between YOY abundance and large crab abundance lagged 2 years.

Figure 30. Relationship between YOY abundance and spawning stock biomass lagged 2 years.

- 87 -

-0.5

0.0

0.5

1.0

1.5

2.0

2.5

0 100 200 300 400 500 600

Natu

ral

Mo

rtali

ty R

ate

M

Recruits (millions)

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10 0.11 0.12 0.13 0.14

Ind

ex o

f R

ecru

its, Y

+1

Index of Spawning Stock Biomass, Y

Low Recruitment SSB Threshold

2009 Predicted Recruitment

Figure 31. Stock Recruitment Model.

Figure 32. Post-hoc estimates of annual M (M = Z - F) as a function of model estimated recruit

abundance.

- 88 -

0.0

0.2

0.4

0.6

0.8

1.0

1.2

LB C-K UB

F

PE0.1 PE0.5 EW OE

Fmax

F0.1

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

19

78

19

80

19

82

19

84

19

86

19

88

19

90

19

92

19

94

19

96

19

98

20

00

20

02

20

04

20

06

20

08

Fis

hin

g M

ort

ali

ty F

Upper Bound F Collie-Kruse F Lower Bound F

Frep

F0.1

Fmax

Figure 33. Average annual F from 1978 to 2006 estimated from three different calculations of exploitation

rates (LB, C-K, UB), across four different error-weighting configurations of the combined-sex CSA model.

Figure 34. Annual upper bound, lower bound, Collie-Kruse F rates in relation to existing F-based

benchmarks (Frep, Fmax, F0.1).

- 89 -

APPENDIX I

MODEL ID: Delaware Bay Blue Crab 2009 combined-sex PE0.1

CSA Version 3.04

Input File: C:\NFT\CSA\2009\RW2009A.DAT

Date of Run: 10-NOV-2009 Time of Run: 11:41

Model Type: Both Process & Observed Error

Process Equation Uses Pope Approximation

Estimated Relative Abundance

Recruits

Year Observed Estimated Residual

1978 0.217941E+01 0.212683E+01 0.244197E-01

1979 0.132930E+01 0.128938E+01 0.304928E-01

1980 0.576796E+01 0.549307E+01 0.488314E-01

1981 0.203026E+01 0.191441E+01 0.587558E-01

1982 0.544537E+00 0.569207E+00 -0.443088E-01

1983 0.883960E+00 0.933150E+00 -0.541546E-01

1984 0.336139E+01 0.311217E+01 0.770345E-01

1985 0.796666E+01 0.707304E+01 0.118975E+00

1986 0.156224E+01 0.160461E+01 -0.267596E-01

1987 0.293568E+01 0.304204E+01 -0.355877E-01

1988 0.386117E+01 0.406525E+01 -0.515048E-01

1989 0.249684E+02 0.210345E+02 0.171448E+00

1990 0.738159E+00 0.845653E+00 -0.135950E+00

1991 0.473937E+01 0.488112E+01 -0.294714E-01

1992 0.373774E+01 0.368663E+01 0.137697E-01

1993 0.817442E+01 0.753893E+01 0.809294E-01

1994 0.112166E+02 0.101118E+02 0.103689E+00

1995 0.264047E+01 0.266025E+01 -0.746446E-02

1996 0.419989E+01 0.415006E+01 0.119364E-01

1997 0.145045E+02 0.128754E+02 0.119144E+00

1998 0.531590E+01 0.513741E+01 0.341539E-01

1999 0.941120E+01 0.857444E+01 0.931152E-01

2000 0.834660E+01 0.747137E+01 0.110776E+00

2001 0.354369E+01 0.333581E+01 0.604535E-01

2002 0.255559E+01 0.243676E+01 0.476150E-01

2003 0.377441E+01 0.356724E+01 0.564509E-01

2004 0.433794E+01 0.417564E+01 0.381331E-01

2005 0.330599E+01 0.293310E+01 0.119677E+00

2006 0.594498E+01 0.568027E+01 0.455483E-01

2007 0.576706E+01 0.524559E+01 0.947739E-01

2008 0.136358E+01 NA NA

Post-Recruits

Year Observed Estimated Residual

1978 0.350253E+00 0.348853E+00 0.400542E-02

1979 0.774146E+00 0.779855E+00 -0.734752E-02

1980 0.468615E+00 0.484104E+00 -0.325173E-01

1981 0.151377E+01 0.151746E+01 -0.243674E-02

1982 0.468927E+00 0.538061E+00 -0.137525E+00

1983 0.546902E+00 0.534491E+00 0.229544E-01

1984 0.964781E+00 0.887277E+00 0.837435E-01

1985 0.608828E+00 0.652211E+00 -0.688317E-01

1986 0.862671E+00 0.978448E+00 -0.125935E+00

1987 0.743671E+00 0.733848E+00 0.132973E-01

1988 0.150844E+01 0.149321E+01 0.101509E-01

1989 0.289848E+01 0.270393E+01 0.694795E-01

1990 0.106490E+01 0.166036E+01 -0.444153E+00

1991 0.131745E+01 0.117342E+01 0.115776E+00

1992 0.249288E+01 0.240914E+01 0.341668E-01

1993 0.145368E+01 0.145118E+01 0.172319E-02

1994 0.139246E+01 0.147650E+01 -0.586004E-01

1995 0.145867E+01 0.160725E+01 -0.970020E-01

1996 0.122760E+01 0.121470E+01 0.105612E-01

1997 0.150668E+01 0.150187E+01 0.319886E-02

1998 0.159025E+01 0.176532E+01 -0.104443E+00

1999 0.154572E+01 0.156894E+01 -0.149133E-01

2000 0.141523E+01 0.151553E+01 -0.684711E-01

2001 0.101673E+01 0.111090E+01 -0.885776E-01

2002 0.717219E+00 0.742191E+00 -0.342250E-01

- 90 -

2003 0.645218E+00 0.668548E+00 -0.355201E-01

2004 0.835094E+00 0.872078E+00 -0.433350E-01

2005 0.120972E+01 0.119221E+01 0.145805E-01

2006 0.367942E+00 0.405134E+00 -0.962932E-01

2007 0.142344E+01 0.143961E+01 -0.112983E-01

2008 0.831015E+00 0.906673E+00 -0.871335E-01

Process Error

Year Calculated Estimated Residual

1978 NA NA NA

1979 0.100930E+01 0.779855E+00 0.815567E-01

1980 0.699598E+00 0.484104E+00 0.116437E+00

1981 0.247722E+01 0.151746E+01 0.154982E+00

1982 0.140022E+01 0.538061E+00 0.302444E+00

1983 0.311558E+00 0.534491E+00 -0.170678E+00

1984 0.478352E+00 0.887277E+00 -0.195369E+00

1985 0.144866E+01 0.652211E+00 0.252357E+00

1986 0.292819E+01 0.978448E+00 0.346640E+00

1987 0.589620E+00 0.733848E+00 -0.691980E-01

1988 0.111654E+01 0.149321E+01 -0.919244E-01

1989 0.168254E+01 0.270393E+01 -0.150019E+00

1990 0.977021E+01 0.166036E+01 0.560452E+00

1991 0.343460E+00 0.117342E+01 -0.388519E+00

1992 0.187308E+01 0.240914E+01 -0.795901E-01

1993 0.166683E+01 0.145118E+01 0.438128E-01

1994 0.308663E+01 0.147650E+01 0.233189E+00

1995 0.405296E+01 0.160725E+01 0.292486E+00

1996 0.113182E+01 0.121470E+01 -0.223497E-01

1997 0.167146E+01 0.150187E+01 0.338326E-01

1998 0.564135E+01 0.176532E+01 0.367390E+00

1999 0.215959E+01 0.156894E+01 0.101039E+00

2000 0.376285E+01 0.151553E+01 0.287582E+00

2001 0.329454E+01 0.111090E+01 0.343771E+00

2002 0.120819E+01 0.742191E+00 0.154090E+00

2003 0.106009E+01 0.668548E+00 0.145780E+00

2004 0.145661E+01 0.872078E+00 0.162222E+00

2005 0.167606E+01 0.119221E+01 0.107720E+00

2006 0.109623E+01 0.405134E+00 0.314779E+00

2007 0.209061E+01 0.143961E+01 0.117979E+00

2008 0.216704E+01 0.906673E+00 0.275540E+00

Input Time of Survey = 0.0000

Input Time of Catch = 0.7500

Input Catchability Ratio

Year SRINIT

1978 1.0000

1979 1.0000

1980 1.0000

1981 1.0000

1982 1.0000

1983 1.0000

1984 1.0000

1985 1.0000

1986 1.0000

1987 1.0000

1988 1.0000

1989 1.0000

1990 1.0000

1991 1.0000

1992 1.0000

1993 1.0000

1994 1.0000

1995 1.0000

1996 1.0000

1997 1.0000

1998 1.0000

1999 1.0000

2000 1.0000

2001 1.0000

2002 1.0000

2003 1.0000

2004 1.0000

2005 1.0000

- 91 -

2006 1.0000

2007 1.0000

2008 1.0000

Catchability Coefficient

Initial Guess: 0.100000E-01

First Pass: 0.386849E-01

Minimum Bound 0.100000E-04

Maximum Bound 0.100000E+02

Post-Bootstrap: 0.047177

Normalized Sum of Squares = 0.336612E-01

Residual Sum of Squares = 0.215432E+01

Variance = 0.742869E-01

Standard Deviation = 0.272556E+00

Weighting Factors for Residuals

Recruits = 1.0000

Post-Recruits = 1.0000

Process Error = 0.1000

Population Estimates

Year Recruits Post-Recruits Total

1978 0.549785E+02 0.901781E+01 0.639963E+02

1979 0.333303E+02 0.201592E+02 0.534895E+02

1980 0.141995E+03 0.125140E+02 0.154509E+03

1981 0.494872E+02 0.392263E+02 0.887135E+02

1982 0.147140E+02 0.139088E+02 0.286228E+02

1983 0.241218E+02 0.138165E+02 0.379384E+02

1984 0.804493E+02 0.229360E+02 0.103385E+03

1985 0.182837E+03 0.168596E+02 0.199697E+03

1986 0.414790E+02 0.252928E+02 0.667718E+02

1987 0.786363E+02 0.189699E+02 0.976062E+02

1988 0.105086E+03 0.385992E+02 0.143686E+03

1989 0.543739E+03 0.698964E+02 0.613636E+03

1990 0.218601E+02 0.429201E+02 0.647802E+02

1991 0.126177E+03 0.303328E+02 0.156509E+03

1992 0.952989E+02 0.622762E+02 0.157575E+03

1993 0.194881E+03 0.375128E+02 0.232393E+03

1994 0.261390E+03 0.381673E+02 0.299557E+03

1995 0.687673E+02 0.415474E+02 0.110315E+03

1996 0.107279E+03 0.314000E+02 0.138679E+03

1997 0.332827E+03 0.388231E+02 0.371650E+03

1998 0.132801E+03 0.456335E+02 0.178435E+03

1999 0.221648E+03 0.405571E+02 0.262205E+03

2000 0.193134E+03 0.391762E+02 0.232310E+03

2001 0.862303E+02 0.287166E+02 0.114947E+03

2002 0.629899E+02 0.191856E+02 0.821755E+02

2003 0.922129E+02 0.172819E+02 0.109495E+03

2004 0.107940E+03 0.225431E+02 0.130483E+03

2005 0.758203E+02 0.308185E+02 0.106639E+03

2006 0.146834E+03 0.104727E+02 0.157307E+03

2007 0.135598E+03 0.372139E+02 0.172812E+03

2008 0.352484E+02 0.234374E+02 0.586858E+02

Biomass Estimates

Year Recruits Post-Recruits Total

1978 0.828674E+00 0.141963E+01 0.224830E+01

1979 0.723964E+00 0.289871E+01 0.362267E+01

1980 0.135524E+01 0.213768E+01 0.349293E+01

1981 0.743086E+00 0.566651E+01 0.640960E+01

1982 0.414076E+00 0.214428E+01 0.255836E+01

1983 0.269870E+00 0.243262E+01 0.270249E+01

1984 0.680936E+00 0.385339E+01 0.453433E+01

1985 0.579028E+00 0.284711E+01 0.342614E+01

1986 0.521963E+00 0.347002E+01 0.399198E+01

1987 0.209306E+00 0.262780E+01 0.283711E+01

1988 0.735140E+00 0.538671E+01 0.612185E+01

1989 0.305169E+01 0.965220E+01 0.127039E+02

1990 0.192042E+00 0.714834E+01 0.734039E+01

1991 0.648630E+00 0.607909E+01 0.672771E+01

1992 0.111848E+01 0.866971E+01 0.978819E+01

1993 0.515635E+00 0.588703E+01 0.640267E+01

- 92 -

1994 0.303633E+00 0.548541E+01 0.578904E+01

1995 0.122076E+00 0.550195E+01 0.562403E+01

1996 0.405133E+00 0.413368E+01 0.453881E+01

1997 0.176616E+01 0.506790E+01 0.683406E+01

1998 0.137653E+01 0.604999E+01 0.742652E+01

1999 0.101213E+01 0.549763E+01 0.650976E+01

2000 0.896546E+00 0.494702E+01 0.584356E+01

2001 0.815819E+00 0.417319E+01 0.498900E+01

2002 0.410776E+00 0.274421E+01 0.315498E+01

2003 0.541857E+00 0.258959E+01 0.313145E+01

2004 0.661260E+00 0.364719E+01 0.430845E+01

2005 0.475921E+00 0.451667E+01 0.499259E+01

2006 0.660338E+00 0.140995E+01 0.207029E+01

2007 0.692150E+00 0.495972E+01 0.565187E+01

2008 0.469262E+00 0.314799E+01 0.361726E+01

Catch Estimate

Year Landings Discards Total

Numbers Numbers Numbers

1978 0.325510E+01 0.000000E+00 0.325510E+01

1979 0.726712E+01 0.000000E+00 0.726712E+01

1980 0.658287E+01 0.000000E+00 0.658287E+01

1981 0.447772E+01 0.000000E+00 0.447772E+01

1982 0.587166E+01 0.000000E+00 0.587166E+01

1983 0.571796E+01 0.000000E+00 0.571796E+01

1984 0.110004E+02 0.000000E+00 0.110004E+02

1985 0.171438E+02 0.000000E+00 0.171438E+02

1986 0.180290E+02 0.000000E+00 0.180290E+02

1987 0.183147E+02 0.000000E+00 0.183147E+02

1988 0.257332E+02 0.000000E+00 0.257332E+02

1989 0.282940E+02 0.000000E+00 0.282940E+02

1990 0.247080E+02 0.000000E+00 0.247080E+02

1991 0.267550E+02 0.000000E+00 0.267550E+02

1992 0.338520E+02 0.000000E+00 0.338520E+02

1993 0.300856E+02 0.000000E+00 0.300856E+02

1994 0.364355E+02 0.000000E+00 0.364355E+02

1995 0.248069E+02 0.000000E+00 0.248069E+02

1996 0.233351E+02 0.000000E+00 0.233351E+02

1997 0.258505E+02 0.000000E+00 0.258505E+02

1998 0.297422E+02 0.000000E+00 0.297422E+02

1999 0.250964E+02 0.000000E+00 0.250964E+02

2000 0.234756E+02 0.000000E+00 0.234756E+02

2001 0.249377E+02 0.000000E+00 0.249377E+02

2002 0.116286E+02 0.000000E+00 0.116286E+02

2003 0.141022E+02 0.000000E+00 0.141022E+02

2004 0.186919E+02 0.000000E+00 0.186919E+02

2005 0.239130E+02 0.000000E+00 0.239130E+02

2006 0.203248E+02 0.000000E+00 0.203248E+02

2007 0.264210E+02 0.000000E+00 0.264210E+02

Catch Estimate

Year Landings Discards Total

Weight Weight Weight

1978 0.502986E+00 0.000000E+00 0.502986E+00

1979 0.112289E+01 0.000000E+00 0.112289E+01

1980 0.100474E+01 0.000000E+00 0.100474E+01

1981 0.715234E+00 0.000000E+00 0.715234E+00

1982 0.921771E+00 0.000000E+00 0.921771E+00

1983 0.893418E+00 0.000000E+00 0.893418E+00

1984 0.171114E+01 0.000000E+00 0.171114E+01

1985 0.261106E+01 0.000000E+00 0.261106E+01

1986 0.272870E+01 0.000000E+00 0.272870E+01

1987 0.271297E+01 0.000000E+00 0.271297E+01

1988 0.384398E+01 0.000000E+00 0.384398E+01

1989 0.425474E+01 0.000000E+00 0.425474E+01

1990 0.391463E+01 0.000000E+00 0.391463E+01

1991 0.389989E+01 0.000000E+00 0.389989E+01

1992 0.516320E+01 0.000000E+00 0.516320E+01

1993 0.450065E+01 0.000000E+00 0.450065E+01

1994 0.530062E+01 0.000000E+00 0.530062E+01

1995 0.379063E+01 0.000000E+00 0.379063E+01

1996 0.352826E+01 0.000000E+00 0.352826E+01

1997 0.386961E+01 0.000000E+00 0.386961E+01

1998 0.459136E+01 0.000000E+00 0.459136E+01

1999 0.393158E+01 0.000000E+00 0.393158E+01

2000 0.370390E+01 0.000000E+00 0.370390E+01

2001 0.391420E+01 0.000000E+00 0.391420E+01

- 93 -

2002 0.183239E+01 0.000000E+00 0.183239E+01

2003 0.223933E+01 0.000000E+00 0.223933E+01

2004 0.294258E+01 0.000000E+00 0.294258E+01

2005 0.377889E+01 0.000000E+00 0.377889E+01

2006 0.315360E+01 0.000000E+00 0.315360E+01

2007 0.412282E+01 0.000000E+00 0.412282E+01

Mortality Estimates

Year Total Natural Fishing

Mortality Mortality Mortality

1978 1.155165 0.800000 0.355165

1979 1.452634 0.800000 0.652634

1980 1.370908 0.800000 0.570908

1981 1.852888 0.800000 1.052888

1982 0.728336 0.800000 -0.071664

1983 0.503254 0.800000 -0.296746

1984 1.813544 0.800000 1.013544

1985 2.066282 0.800000 1.266282

1986 1.258428 0.800000 0.458428

1987 0.927709 0.800000 0.127709

1988 0.720613 0.800000 -0.079387

1989 2.660061 0.800000 1.860061

1990 0.758770 0.800000 -0.041230

1991 0.921537 0.800000 0.121537

1992 1.435220 0.800000 0.635220

1993 1.806452 0.800000 1.006452

1994 1.975471 0.800000 1.175471

1995 1.256530 0.800000 0.456530

1996 1.273142 0.800000 0.473142

1997 2.097311 0.800000 1.297311

1998 1.481514 0.800000 0.681514

1999 1.901058 0.800000 1.101058

2000 2.090599 0.800000 1.290599

2001 1.790313 0.800000 0.990313

2002 1.559197 0.800000 0.759197

2003 1.580446 0.800000 0.780446

2004 1.443127 0.800000 0.643127

2005 2.320677 0.800000 1.520677

2006 1.441518 0.800000 0.641518

2007 1.997871 0.800000 1.197871

Average Mortality (1978 - 2007)

Z F

1.521353 0.721353

Harvest Rate Estimates

Year Combined Landings Derived F

1978 0.926801E-01 0.926801E-01 0.143157

1979 0.247555E+00 0.247555E+00 0.430304

1980 0.776314E-01 0.776314E-01 0.118675

1981 0.919696E-01 0.919696E-01 0.141989

1982 0.373788E+00 0.373788E+00 0.729942

1983 0.274624E+00 0.274624E+00 0.488543

1984 0.193878E+00 0.193878E+00 0.322654

1985 0.156427E+00 0.156427E+00 0.252977

1986 0.491988E+00 0.491988E+00 1.098667

1987 0.341901E+00 0.341901E+00 0.646918

1988 0.326331E+00 0.326331E+00 0.608363

1989 0.840158E-01 0.840158E-01 0.128998

1990 0.694979E+00 0.694979E+00 2.184839

1991 0.311488E+00 0.311488E+00 0.572725

1992 0.391447E+00 0.391447E+00 0.778485

1993 0.235891E+00 0.235891E+00 0.406065

1994 0.221627E+00 0.221627E+00 0.377080

1995 0.409748E+00 0.409748E+00 0.830916

1996 0.306604E+00 0.306604E+00 0.561225

1997 0.126740E+00 0.126740E+00 0.200545

1998 0.303718E+00 0.303718E+00 0.554481

1999 0.174400E+00 0.174400E+00 0.285901

2000 0.184130E+00 0.184130E+00 0.304117

2001 0.395308E+00 0.395308E+00 0.789362

2002 0.257847E+00 0.257847E+00 0.452112

2003 0.234676E+00 0.234676E+00 0.403568

2004 0.261022E+00 0.261022E+00 0.458921

2005 0.408597E+00 0.408597E+00 0.827553

- 94 -

2006 0.235426E+00 0.235426E+00 0.405109

2007 0.278582E+00 0.278582E+00 0.497301

Surplus Production

Average Adjustment Factor (Delta) = 1.0000

Year Biomass Delta Biomass Catch Biomass Surplus Production

1978 2.248 1.374 0.503 1.877

1979 3.623 -0.130 1.123 0.993

1980 3.493 2.917 1.005 3.921

1981 6.410 -3.851 0.715 -3.136

1982 2.558 0.144 0.922 1.066

1983 2.702 1.832 0.893 2.725

1984 4.534 -1.108 1.711 0.603

1985 3.426 0.566 2.611 3.177

1986 3.992 -1.155 2.729 1.574

1987 2.837 3.285 2.713 5.998

1988 6.122 6.582 3.844 10.426

1989 12.704 -5.364 4.255 -1.109

1990 7.340 -0.613 3.915 3.302

1991 6.728 3.060 3.900 6.960

1992 9.788 -3.386 5.163 1.778

1993 6.403 -0.614 4.501 3.887

1994 5.789 -0.165 5.301 5.136

1995 5.624 -1.085 3.791 2.705

1996 4.539 2.295 3.528 5.824

1997 6.834 0.592 3.870 4.462

1998 7.427 -0.917 4.591 3.675

1999 6.510 -0.666 3.932 3.265

2000 5.844 -0.855 3.704 2.849

2001 4.989 -1.834 3.914 2.080

2002 3.155 -0.024 1.832 1.809

2003 3.131 1.177 2.239 3.416

2004 4.308 0.684 2.943 3.627

2005 4.993 -2.922 3.779 0.857

2006 2.070 3.582 3.154 6.735

2007 5.652 -2.035 4.123 2.088

2008 3.617

Levenburg-Marquadt NLLS Parameter Statistical Summary

Parameter Parameter Est. Std. Error CV

1 R 1978 0.212683E+01 0.557451E+00 0.262104E+00

2 R 1979 0.128938E+01 0.341290E+00 0.264693E+00

3 R 1980 0.549307E+01 0.143385E+01 0.261029E+00

4 R 1981 0.191441E+01 0.513205E+00 0.268075E+00

5 R 1982 0.569207E+00 0.150975E+00 0.265237E+00

6 R 1983 0.933150E+00 0.246206E+00 0.263843E+00

7 R 1984 0.311217E+01 0.814876E+00 0.261836E+00

8 R 1985 0.707304E+01 0.183254E+01 0.259088E+00

9 R 1986 0.160461E+01 0.414020E+00 0.258019E+00

10 R 1987 0.304204E+01 0.779789E+00 0.256338E+00

11 R 1988 0.406525E+01 0.105518E+01 0.259561E+00

12 R 1989 0.210345E+02 0.550246E+01 0.261593E+00

13 R 1990 0.845653E+00 0.225432E+00 0.266578E+00

14 R 1991 0.488112E+01 0.125698E+01 0.257518E+00

15 R 1992 0.368663E+01 0.965844E+00 0.261986E+00

16 R 1993 0.753893E+01 0.195227E+01 0.258959E+00

17 R 1994 0.101118E+02 0.261248E+01 0.258359E+00

18 R 1995 0.266025E+01 0.693727E+00 0.260775E+00

19 R 1996 0.415006E+01 0.107391E+01 0.258770E+00

20 R 1997 0.128754E+02 0.335313E+01 0.260430E+00

21 R 1998 0.513741E+01 0.133482E+01 0.259825E+00

22 R 1999 0.857444E+01 0.223384E+01 0.260523E+00

23 R 2000 0.747137E+01 0.194738E+01 0.260645E+00

24 R 2001 0.333581E+01 0.854945E+00 0.256293E+00

25 R 2002 0.243676E+01 0.634778E+00 0.260501E+00

26 R 2003 0.356724E+01 0.923496E+00 0.258882E+00

27 R 2004 0.417564E+01 0.107944E+01 0.258509E+00

28 R 2005 0.293310E+01 0.754890E+00 0.257370E+00

29 R 2006 0.568027E+01 0.145394E+01 0.255963E+00

30 R 2007 0.524559E+01 0.136020E+01 0.259303E+00

31 N 1978 0.348853E+00 0.949858E-01 0.272280E+00

32 N 1979 0.779855E+00 0.201475E+00 0.258349E+00

- 95 -

33 N 1980 0.484104E+00 0.126317E+00 0.260929E+00

34 N 1981 0.151746E+01 0.392241E+00 0.258485E+00

35 N 1982 0.538061E+00 0.137062E+00 0.254733E+00

36 N 1983 0.534491E+00 0.138352E+00 0.258847E+00

37 N 1984 0.887277E+00 0.230997E+00 0.260344E+00

38 N 1985 0.652211E+00 0.170176E+00 0.260921E+00

39 N 1986 0.978448E+00 0.250689E+00 0.256211E+00

40 N 1987 0.733848E+00 0.192091E+00 0.261759E+00

41 N 1988 0.149321E+01 0.388360E+00 0.260085E+00

42 N 1989 0.270393E+01 0.706685E+00 0.261355E+00

43 N 1990 0.166036E+01 0.397151E+00 0.239196E+00

44 N 1991 0.117342E+01 0.312519E+00 0.266332E+00

45 N 1992 0.240914E+01 0.619767E+00 0.257256E+00

46 N 1993 0.145118E+01 0.379209E+00 0.261312E+00

47 N 1994 0.147650E+01 0.385392E+00 0.261018E+00

48 N 1995 0.160725E+01 0.413547E+00 0.257300E+00

49 N 1996 0.121470E+01 0.316741E+00 0.260756E+00

50 N 1997 0.150187E+01 0.392549E+00 0.261374E+00

51 N 1998 0.176532E+01 0.458448E+00 0.259696E+00

52 N 1999 0.156894E+01 0.409585E+00 0.261058E+00

53 N 2000 0.151553E+01 0.395013E+00 0.260644E+00

54 N 2001 0.111090E+01 0.288182E+00 0.259414E+00

55 N 2002 0.742191E+00 0.193684E+00 0.260962E+00

56 N 2003 0.668548E+00 0.174360E+00 0.260805E+00

57 N 2004 0.872078E+00 0.227373E+00 0.260725E+00

58 N 2005 0.119221E+01 0.308753E+00 0.258975E+00

59 N 2006 0.405134E+00 0.106156E+00 0.262026E+00

60 N 2007 0.143961E+01 0.375160E+00 0.260598E+00

61 N 2008 0.906673E+00 0.237002E+00 0.261397E+00

62 Q 0.386849E-01 0.119542E-01 0.309015E+00

Model Type: Both Process & Observed Error

Error Type: Parametric Log-Normal Error With Bias

Number of Bootstraps: 2000

-- Non-Linear Least Squares Fit --

Maximum Monte-Carlo Iterations = 200

Scaled Gradient Tolerance = 0.3450E-03

Scaled Step Tolerance = 0.2420E-04

Relative Function Tolerance = 0.2420E-07

Absolute Function Tolerance = 0.1420E-13

Bootstrap Summary Report

Number of Bootstrap Repitions Requested = 2000

Number of Bootstrap Repititions Completed = 2000

Number of Bootstrap Repititions Not Converged = 0

Number of Bootstrap Repititions Infeasible F = 0

Bootstrap Output Variable: Recruit Abundance

Year NLLS Bootstrap Bootstrap C.V. For

Estimate Mean Std Error Bootstrap

1978 0.549785E+02 0.478866E+02 0.146707E+02 0.306363E+00

1979 0.333303E+02 0.292157E+02 0.866799E+01 0.296690E+00

1980 0.141995E+03 0.121675E+03 0.366025E+02 0.300822E+00

1981 0.494872E+02 0.428053E+02 0.132450E+02 0.309423E+00

1982 0.147140E+02 0.137037E+02 0.401864E+01 0.293252E+00

1983 0.241218E+02 0.229276E+02 0.659457E+01 0.287625E+00

1984 0.804493E+02 0.677793E+02 0.203275E+02 0.299907E+00

1985 0.182837E+03 0.147534E+03 0.426079E+02 0.288800E+00

1986 0.414790E+02 0.380916E+02 0.100412E+02 0.263607E+00

1987 0.786363E+02 0.727584E+02 0.189899E+02 0.260999E+00

1988 0.105086E+03 0.100293E+03 0.276969E+02 0.276161E+00

1989 0.543739E+03 0.426339E+03 0.123478E+03 0.289623E+00

1990 0.218601E+02 0.211005E+02 0.602523E+01 0.285549E+00

1991 0.126177E+03 0.116941E+03 0.314751E+02 0.269154E+00

1992 0.952989E+02 0.854089E+02 0.231935E+02 0.271558E+00

1993 0.194881E+03 0.164358E+03 0.475953E+02 0.289583E+00

1994 0.261390E+03 0.216732E+03 0.638615E+02 0.294656E+00

1995 0.687673E+02 0.623417E+02 0.170113E+02 0.272872E+00

1996 0.107279E+03 0.952008E+02 0.275347E+02 0.289228E+00

1997 0.332827E+03 0.268220E+03 0.813312E+02 0.303225E+00

1998 0.132801E+03 0.117180E+03 0.332993E+02 0.284171E+00

- 96 -

1999 0.221648E+03 0.183104E+03 0.555609E+02 0.303439E+00

2000 0.193134E+03 0.158132E+03 0.477829E+02 0.302170E+00

2001 0.862303E+02 0.740453E+02 0.203571E+02 0.274927E+00

2002 0.629899E+02 0.540673E+02 0.155985E+02 0.288502E+00

2003 0.922129E+02 0.786274E+02 0.229186E+02 0.291484E+00

2004 0.107940E+03 0.938062E+02 0.276837E+02 0.295116E+00

2005 0.758203E+02 0.619646E+02 0.173248E+02 0.279593E+00

2006 0.146834E+03 0.128389E+03 0.359298E+02 0.279851E+00

2007 0.135598E+03 0.113158E+03 0.329183E+02 0.290906E+00

2008 0.352484E+02 0.295522E+02 0.462638E+01 0.156549E+00

NLLS

Estimate C.V. For

Bias Bias Per Cent Corrected Corrected

Year Estimate Std. Error Bias For Bias Estimate

1978 -0.7092E+01 0.3644E+00 -12.899373 0.6207E+02 0.2364E+00

1979 -0.4115E+01 0.2146E+00 -12.345013 0.3744E+02 0.2315E+00

1980 -0.2032E+02 0.9362E+00 -14.310564 0.1623E+03 0.2255E+00

1981 -0.6682E+01 0.3317E+00 -13.502405 0.5617E+02 0.2358E+00

1982 -0.1010E+01 0.9266E-01 -6.865993 0.1572E+02 0.2556E+00

1983 -0.1194E+01 0.1499E+00 -4.950862 0.2532E+02 0.2605E+00

1984 -0.1267E+02 0.5356E+00 -15.748978 0.9312E+02 0.2183E+00

1985 -0.3530E+02 0.1237E+01 -19.308393 0.2181E+03 0.1953E+00

1986 -0.3387E+01 0.2370E+00 -8.166450 0.4487E+02 0.2238E+00

1987 -0.5878E+01 0.4445E+00 -7.474824 0.8451E+02 0.2247E+00

1988 -0.4794E+01 0.6285E+00 -4.561720 0.1099E+03 0.2521E+00

1989 -0.1174E+03 0.3810E+01 -21.591297 0.6611E+03 0.1868E+00

1990 -0.7596E+00 0.1358E+00 -3.474616 0.2262E+02 0.2664E+00

1991 -0.9236E+01 0.7335E+00 -7.319665 0.1354E+03 0.2324E+00

1992 -0.9890E+01 0.5638E+00 -10.377910 0.1052E+03 0.2205E+00

1993 -0.3052E+02 0.1264E+01 -15.662242 0.2254E+03 0.2112E+00

1994 -0.4466E+02 0.1743E+01 -17.084537 0.3060E+03 0.2087E+00

1995 -0.6426E+01 0.4066E+00 -9.343971 0.7519E+02 0.2262E+00

1996 -0.1208E+02 0.6723E+00 -11.258345 0.1194E+03 0.2307E+00

1997 -0.6461E+02 0.2323E+01 -19.411372 0.3974E+03 0.2046E+00

1998 -0.1562E+02 0.8225E+00 -11.762704 0.1484E+03 0.2244E+00

1999 -0.3854E+02 0.1512E+01 -17.389845 0.2602E+03 0.2135E+00

2000 -0.3500E+02 0.1325E+01 -18.123011 0.2281E+03 0.2094E+00

2001 -0.1218E+02 0.5305E+00 -14.130742 0.9842E+02 0.2068E+00

2002 -0.8923E+01 0.4019E+00 -14.165215 0.7191E+02 0.2169E+00

2003 -0.1359E+02 0.5958E+00 -14.732791 0.1058E+03 0.2166E+00

2004 -0.1413E+02 0.6951E+00 -13.093947 0.1221E+03 0.2268E+00

2005 -0.1386E+02 0.4961E+00 -18.274366 0.8968E+02 0.1932E+00

2006 -0.1845E+02 0.9031E+00 -12.561966 0.1653E+03 0.2174E+00

2007 -0.2244E+02 0.8909E+00 -16.549045 0.1580E+03 0.2083E+00

2008 -0.5696E+01 0.1641E+00 -16.160064 0.4094E+02 0.1130E+00

Year 5. % Percentile 95. % Percentile

1978 0.286267E+02 0.750380E+02

1979 0.174700E+02 0.451571E+02

1980 0.724467E+02 0.187907E+03

1981 0.251921E+02 0.668098E+02

1982 0.840608E+01 0.213467E+02

1983 0.140707E+02 0.351199E+02

1984 0.407872E+02 0.104829E+03

1985 0.886915E+02 0.224939E+03

1986 0.246616E+02 0.567517E+02

1987 0.472130E+02 0.109296E+03

1988 0.646600E+02 0.152796E+03

1989 0.263140E+03 0.651616E+03

1990 0.125110E+02 0.320236E+02

1991 0.758971E+02 0.175376E+03

1992 0.544853E+02 0.126651E+03

1993 0.100279E+03 0.249133E+03

1994 0.131809E+03 0.333292E+03

1995 0.395424E+02 0.936470E+02

1996 0.601292E+02 0.147562E+03

1997 0.161742E+03 0.419784E+03

1998 0.731563E+02 0.178577E+03

1999 0.110335E+03 0.284314E+03

2000 0.932286E+02 0.244585E+03

2001 0.484813E+02 0.112123E+03

2002 0.333964E+02 0.826499E+02

2003 0.492243E+02 0.119556E+03

2004 0.575816E+02 0.146444E+03

- 97 -

2005 0.402105E+02 0.938528E+02

2006 0.800361E+02 0.194776E+03

2007 0.691867E+02 0.172502E+03

2008 0.234750E+02 0.380624E+02

Bootstrap Output Variable: Post-Recruit Abundance

Year NLLS Bootstrap Bootstrap C.V. For

Estimate Mean Std Error Bootstrap

1978 0.901781E+01 0.813393E+01 0.253182E+01 0.311266E+00

1979 0.201592E+02 0.180822E+02 0.535190E+01 0.295975E+00

1980 0.125140E+02 0.114457E+02 0.358191E+01 0.312949E+00

1981 0.392263E+02 0.349955E+02 0.101525E+02 0.290108E+00

1982 0.139088E+02 0.139484E+02 0.378285E+01 0.271204E+00

1983 0.138165E+02 0.122001E+02 0.380176E+01 0.311618E+00

1984 0.229360E+02 0.191832E+02 0.601343E+01 0.313473E+00

1985 0.168596E+02 0.160452E+02 0.494374E+01 0.308113E+00

1986 0.252928E+02 0.254152E+02 0.706137E+01 0.277841E+00

1987 0.189699E+02 0.169218E+02 0.538372E+01 0.318154E+00

1988 0.385992E+02 0.342251E+02 0.106349E+02 0.310733E+00

1989 0.698964E+02 0.591359E+02 0.179328E+02 0.303246E+00

1990 0.429201E+02 0.500054E+02 0.853776E+01 0.170737E+00

1991 0.303328E+02 0.256234E+02 0.840874E+01 0.328167E+00

1992 0.622762E+02 0.546699E+02 0.161318E+02 0.295076E+00

1993 0.375128E+02 0.336555E+02 0.107759E+02 0.320183E+00

1994 0.381673E+02 0.361394E+02 0.112547E+02 0.311424E+00

1995 0.415474E+02 0.402078E+02 0.118233E+02 0.294054E+00

1996 0.314000E+02 0.279907E+02 0.866827E+01 0.309684E+00

1997 0.388231E+02 0.347859E+02 0.106540E+02 0.306275E+00

1998 0.456335E+02 0.443281E+02 0.131215E+02 0.296008E+00

1999 0.405571E+02 0.370269E+02 0.116677E+02 0.315114E+00

2000 0.391762E+02 0.370920E+02 0.112344E+02 0.302880E+00

2001 0.287166E+02 0.277724E+02 0.826480E+01 0.297591E+00

2002 0.191856E+02 0.177919E+02 0.577611E+01 0.324648E+00

2003 0.172819E+02 0.159274E+02 0.501933E+01 0.315138E+00

2004 0.225431E+02 0.211203E+02 0.662957E+01 0.313896E+00

2005 0.308185E+02 0.276112E+02 0.841529E+01 0.304778E+00

2006 0.104727E+02 0.101442E+02 0.343256E+01 0.338375E+00

2007 0.372139E+02 0.335104E+02 0.995321E+01 0.297019E+00

2008 0.234374E+02 0.228318E+02 0.741163E+01 0.324618E+00

NLLS

Estimate C.V. For

Bias Bias Per Cent Corrected Corrected

Year Estimate Std. Error Bias For Bias Estimate

1978 -0.8839E+00 0.5997E-01 -9.801518 0.9902E+01 0.2557E+00

1979 -0.2077E+01 0.1284E+00 -10.302679 0.2224E+02 0.2407E+00

1980 -0.1068E+01 0.8358E-01 -8.537149 0.1358E+02 0.2637E+00

1981 -0.4231E+01 0.2459E+00 -10.785586 0.4346E+02 0.2336E+00

1982 0.3952E-01 0.8459E-01 0.284166 0.1387E+02 0.2727E+00

1983 -0.1616E+01 0.9238E-01 -11.699591 0.1543E+02 0.2463E+00

1984 -0.3753E+01 0.1585E+00 -16.361980 0.2669E+02 0.2253E+00

1985 -0.8143E+00 0.1120E+00 -4.830113 0.1767E+02 0.2797E+00

1986 0.1224E+00 0.1579E+00 0.483830 0.2517E+02 0.2805E+00

1987 -0.2048E+01 0.1288E+00 -10.796641 0.2102E+02 0.2561E+00

1988 -0.4374E+01 0.2571E+00 -11.332043 0.4297E+02 0.2475E+00

1989 -0.1076E+02 0.4677E+00 -15.394839 0.8066E+02 0.2223E+00

1990 0.7085E+01 0.2481E+00 16.508185 0.3583E+02 0.2383E+00

1991 -0.4709E+01 0.2155E+00 -15.525870 0.3504E+02 0.2400E+00

1992 -0.7606E+01 0.3988E+00 -12.213786 0.6988E+02 0.2308E+00

1993 -0.3857E+01 0.2559E+00 -10.282524 0.4137E+02 0.2605E+00

1994 -0.2028E+01 0.2557E+00 -5.313214 0.4020E+02 0.2800E+00

1995 -0.1340E+01 0.2661E+00 -3.224133 0.4289E+02 0.2757E+00

1996 -0.3409E+01 0.2083E+00 -10.857615 0.3481E+02 0.2490E+00

1997 -0.4037E+01 0.2548E+00 -10.399041 0.4286E+02 0.2486E+00

1998 -0.1305E+01 0.2949E+00 -2.860478 0.4694E+02 0.2795E+00

1999 -0.3530E+01 0.2726E+00 -8.704106 0.4409E+02 0.2647E+00

2000 -0.2084E+01 0.2555E+00 -5.320094 0.4126E+02 0.2723E+00

2001 -0.9442E+00 0.1860E+00 -3.288141 0.2966E+02 0.2786E+00

2002 -0.1394E+01 0.1329E+00 -7.264053 0.2058E+02 0.2807E+00

2003 -0.1354E+01 0.1163E+00 -7.837539 0.1864E+02 0.2693E+00

2004 -0.1423E+01 0.1516E+00 -6.311781 0.2397E+02 0.2766E+00

2005 -0.3207E+01 0.2014E+00 -10.407095 0.3403E+02 0.2473E+00

2006 -0.3285E+00 0.7711E-01 -3.136281 0.1080E+02 0.3178E+00

2007 -0.3703E+01 0.2375E+00 -9.951867 0.4092E+02 0.2433E+00

- 98 -

2008 -0.6056E+00 0.1663E+00 -2.583756 0.2404E+02 0.3083E+00

Year 5. % Percentile 95. % Percentile

1978 0.483456E+01 0.126141E+02

1979 0.109687E+02 0.278404E+02

1980 0.653905E+01 0.177353E+02

1981 0.213309E+02 0.536100E+02

1982 0.872924E+01 0.207743E+02

1983 0.717332E+01 0.193676E+02

1984 0.113084E+02 0.304909E+02

1985 0.925141E+01 0.252718E+02

1986 0.157587E+02 0.387294E+02

1987 0.986766E+01 0.272322E+02

1988 0.200072E+02 0.534406E+02

1989 0.352182E+02 0.903981E+02

1990 0.371543E+02 0.645311E+02

1991 0.148879E+02 0.409789E+02

1992 0.326723E+02 0.844813E+02

1993 0.193712E+02 0.531146E+02

1994 0.211016E+02 0.571310E+02

1995 0.245169E+02 0.621994E+02

1996 0.165077E+02 0.439186E+02

1997 0.207304E+02 0.547576E+02

1998 0.270469E+02 0.688407E+02

1999 0.214809E+02 0.579127E+02

2000 0.223071E+02 0.579945E+02

2001 0.166131E+02 0.427418E+02

2002 0.101170E+02 0.284465E+02

2003 0.932091E+01 0.250219E+02

2004 0.124376E+02 0.333230E+02

2005 0.163719E+02 0.436430E+02

2006 0.563598E+01 0.159735E+02

2007 0.197358E+02 0.515705E+02

2008 0.133848E+02 0.369728E+02

Bootstrap Output Variable: Total Abundance

Year NLLS Bootstrap Bootstrap C.V. For

Estimate Mean Std Error Bootstrap

1978 0.639963E+02 0.560205E+02 0.154840E+02 0.276399E+00

1979 0.534895E+02 0.472979E+02 0.112534E+02 0.237927E+00

1980 0.154509E+03 0.133121E+03 0.377478E+02 0.283561E+00

1981 0.887135E+02 0.778008E+02 0.186640E+02 0.239895E+00

1982 0.286228E+02 0.276521E+02 0.578458E+01 0.209192E+00

1983 0.379384E+02 0.351277E+02 0.830703E+01 0.236481E+00

1984 0.103385E+03 0.869626E+02 0.228880E+02 0.263194E+00

1985 0.199697E+03 0.163580E+03 0.442210E+02 0.270333E+00

1986 0.667718E+02 0.635068E+02 0.121047E+02 0.190604E+00

1987 0.976062E+02 0.896802E+02 0.205632E+02 0.229294E+00

1988 0.143686E+03 0.134518E+03 0.313848E+02 0.233314E+00

1989 0.613636E+03 0.485475E+03 0.128899E+03 0.265512E+00

1990 0.647802E+02 0.711059E+02 0.762403E+01 0.107221E+00

1991 0.156509E+03 0.142564E+03 0.342924E+02 0.240540E+00

1992 0.157575E+03 0.140079E+03 0.304377E+02 0.217290E+00

1993 0.232393E+03 0.198013E+03 0.520178E+02 0.262698E+00

1994 0.299557E+03 0.252872E+03 0.677153E+02 0.267785E+00

1995 0.110315E+03 0.102550E+03 0.215807E+02 0.210442E+00

1996 0.138679E+03 0.123191E+03 0.308210E+02 0.250188E+00

1997 0.371650E+03 0.303006E+03 0.850661E+02 0.280740E+00

1998 0.178435E+03 0.161509E+03 0.383947E+02 0.237726E+00

1999 0.262205E+03 0.220131E+03 0.600346E+02 0.272722E+00

2000 0.232310E+03 0.195224E+03 0.519709E+02 0.266211E+00

2001 0.114947E+03 0.101818E+03 0.235132E+02 0.230934E+00

2002 0.821755E+02 0.718592E+02 0.181634E+02 0.252763E+00

2003 0.109495E+03 0.945548E+02 0.249309E+02 0.263667E+00

2004 0.130483E+03 0.114926E+03 0.299107E+02 0.260259E+00

2005 0.106639E+03 0.895758E+02 0.215048E+02 0.240074E+00

2006 0.157307E+03 0.138533E+03 0.371620E+02 0.268253E+00

2007 0.172812E+03 0.146668E+03 0.366185E+02 0.249669E+00

2008 0.586858E+02 0.523841E+02 0.107651E+02 0.205502E+00

NLLS

Estimate C.V. For

Bias Bias Per Cent Corrected Corrected

Year Estimate Std. Error Bias For Bias Estimate

- 99 -

1978 -0.7976E+01 0.3895E+00 -0.3547E+03 0.7197E+02 0.2151E+00

1979 -0.6192E+01 0.2872E+00 -0.1709E+03 0.5968E+02 0.1886E+00

1980 -0.2139E+02 0.9702E+00 -0.6123E+03 0.1759E+03 0.2146E+00

1981 -0.1091E+02 0.4835E+00 -0.1703E+03 0.9963E+02 0.1873E+00

1982 -0.9707E+00 0.1312E+00 -0.3794E+02 0.2959E+02 0.1955E+00

1983 -0.2811E+01 0.1961E+00 -0.1040E+03 0.4075E+02 0.2039E+00

1984 -0.1642E+02 0.6300E+00 -0.3622E+03 0.1198E+03 0.1910E+00

1985 -0.3612E+02 0.1277E+01 -0.1054E+04 0.2358E+03 0.1875E+00

1986 -0.3265E+01 0.2803E+00 -0.8179E+02 0.7004E+02 0.1728E+00

1987 -0.7926E+01 0.4928E+00 -0.2794E+03 0.1055E+03 0.1949E+00

1988 -0.9168E+01 0.7311E+00 -0.1498E+03 0.1529E+03 0.2053E+00

1989 -0.1282E+03 0.4065E+01 -0.1009E+04 0.7418E+03 0.1738E+00

1990 0.6326E+01 0.2215E+00 0.8618E+02 0.5845E+02 0.1304E+00

1991 -0.1395E+02 0.8278E+00 -0.2073E+03 0.1705E+03 0.2012E+00

1992 -0.1750E+02 0.7851E+00 -0.1787E+03 0.1751E+03 0.1739E+00

1993 -0.3438E+02 0.1394E+01 -0.5370E+03 0.2668E+03 0.1950E+00

1994 -0.4669E+02 0.1839E+01 -0.8064E+03 0.3462E+03 0.1956E+00

1995 -0.7765E+01 0.5129E+00 -0.1381E+03 0.1181E+03 0.1828E+00

1996 -0.1549E+02 0.7713E+00 -0.3412E+03 0.1542E+03 0.1999E+00

1997 -0.6864E+02 0.2444E+01 -0.1004E+04 0.4403E+03 0.1932E+00

1998 -0.1693E+02 0.9383E+00 -0.2279E+03 0.1954E+03 0.1965E+00

1999 -0.4207E+02 0.1639E+01 -0.6463E+03 0.3043E+03 0.1973E+00

2000 -0.3709E+02 0.1428E+01 -0.6346E+03 0.2694E+03 0.1929E+00

2001 -0.1313E+02 0.6022E+00 -0.2632E+03 0.1281E+03 0.1836E+00

2002 -0.1032E+02 0.4671E+00 -0.3270E+03 0.9249E+02 0.1964E+00

2003 -0.1494E+02 0.6499E+00 -0.4771E+03 0.1244E+03 0.2004E+00

2004 -0.1556E+02 0.7539E+00 -0.3611E+03 0.1460E+03 0.2048E+00

2005 -0.1706E+02 0.6139E+00 -0.3418E+03 0.1237E+03 0.1738E+00

2006 -0.1877E+02 0.9310E+00 -0.9068E+03 0.1761E+03 0.2111E+00

2007 -0.2614E+02 0.1006E+01 -0.4626E+03 0.1990E+03 0.1841E+00

2008 -0.6302E+01 0.2789E+00 -0.1742E+03 0.6499E+02 0.1656E+00

Year 5. % Percentile 95. % Percentile

1978 0.356443E+02 0.847245E+02

1979 0.317679E+02 0.675371E+02

1980 0.823243E+02 0.200361E+03

1981 0.521271E+02 0.111351E+03

1982 0.202894E+02 0.382856E+02

1983 0.241183E+02 0.503037E+02

1984 0.564350E+02 0.128179E+03

1985 0.102578E+03 0.244231E+03

1986 0.486778E+02 0.875123E+02

1987 0.627852E+02 0.129122E+03

1988 0.940558E+02 0.194387E+03

1989 0.313984E+03 0.715771E+03

1990 0.613487E+02 0.849577E+02

1991 0.974726E+02 0.208304E+03

1992 0.101472E+03 0.198913E+03

1993 0.128817E+03 0.291500E+03

1994 0.163010E+03 0.377174E+03

1995 0.749135E+02 0.142961E+03

1996 0.844129E+02 0.179707E+03

1997 0.191441E+03 0.463839E+03

1998 0.109801E+03 0.231440E+03

1999 0.142629E+03 0.330049E+03

2000 0.125338E+03 0.289022E+03

2001 0.722128E+02 0.145844E+03

2002 0.471062E+02 0.105902E+03

2003 0.628230E+02 0.139287E+03

2004 0.753817E+02 0.170456E+03

2005 0.627421E+02 0.129156E+03

2006 0.890124E+02 0.207331E+03

2007 0.985730E+02 0.214013E+03

2008 0.382215E+02 0.721383E+02

Bootstrap Output Variable: Recruit Biomass

Year NLLS Bootstrap Bootstrap C.V. For

Estimate Mean Std Error Bootstrap

1978 0.828674E+00 0.721780E+00 0.221127E+00 0.306363E+00

1979 0.723964E+00 0.634590E+00 0.188276E+00 0.296690E+00

1980 0.135524E+01 0.116130E+01 0.349345E+00 0.300822E+00

1981 0.743086E+00 0.642751E+00 0.198882E+00 0.309423E+00

1982 0.414076E+00 0.385645E+00 0.113091E+00 0.293252E+00

- 100 -

1983 0.269870E+00 0.256510E+00 0.737787E-01 0.287625E+00

1984 0.680936E+00 0.573695E+00 0.172055E+00 0.299907E+00

1985 0.579028E+00 0.467227E+00 0.134935E+00 0.288800E+00

1986 0.521963E+00 0.479338E+00 0.126357E+00 0.263607E+00

1987 0.209306E+00 0.193660E+00 0.505452E-01 0.260999E+00

1988 0.735140E+00 0.701605E+00 0.193756E+00 0.276161E+00

1989 0.305169E+01 0.239279E+01 0.693008E+00 0.289623E+00

1990 0.192042E+00 0.185369E+00 0.529320E-01 0.285549E+00

1991 0.648630E+00 0.601152E+00 0.161803E+00 0.269154E+00

1992 0.111848E+01 0.100240E+01 0.272210E+00 0.271558E+00

1993 0.515635E+00 0.434875E+00 0.125933E+00 0.289583E+00

1994 0.303633E+00 0.251759E+00 0.741822E-01 0.294656E+00

1995 0.122076E+00 0.110670E+00 0.301987E-01 0.272872E+00

1996 0.405133E+00 0.359522E+00 0.103984E+00 0.289228E+00

1997 0.176616E+01 0.142333E+01 0.431589E+00 0.303225E+00

1998 0.137653E+01 0.121461E+01 0.345157E+00 0.284171E+00

1999 0.101213E+01 0.836123E+00 0.253712E+00 0.303439E+00

2000 0.896546E+00 0.734065E+00 0.221813E+00 0.302170E+00

2001 0.815819E+00 0.700538E+00 0.192597E+00 0.274927E+00

2002 0.410776E+00 0.352589E+00 0.101723E+00 0.288502E+00

2003 0.541857E+00 0.462026E+00 0.134673E+00 0.291484E+00

2004 0.661260E+00 0.574675E+00 0.169596E+00 0.295116E+00

2005 0.475921E+00 0.388949E+00 0.108747E+00 0.279593E+00

2006 0.660338E+00 0.577387E+00 0.161582E+00 0.279851E+00

2007 0.692150E+00 0.577606E+00 0.168029E+00 0.290906E+00

2008 0.469262E+00 0.393429E+00 0.615910E-01 0.156549E+00

NLLS

Estimate C.V. For

Bias Bias Per Cent Corrected Corrected

Year Estimate Std. Error Bias For Bias Estimate

1978 -0.1069E+00 0.5492E-02 -0.1290E+02 0.9356E+00 0.2364E+00

1979 -0.8937E-01 0.4660E-02 -0.1235E+02 0.8133E+00 0.2315E+00

1980 -0.1939E+00 0.8935E-02 -0.1431E+02 0.1549E+01 0.2255E+00

1981 -0.1003E+00 0.4981E-02 -0.1350E+02 0.8434E+00 0.2358E+00

1982 -0.2843E-01 0.2608E-02 -0.6866E+01 0.4425E+00 0.2556E+00

1983 -0.1336E-01 0.1677E-02 -0.4951E+01 0.2832E+00 0.2605E+00

1984 -0.1072E+00 0.4534E-02 -0.1575E+02 0.7882E+00 0.2183E+00

1985 -0.1118E+00 0.3919E-02 -0.1931E+02 0.6908E+00 0.1953E+00

1986 -0.4263E-01 0.2982E-02 -0.8166E+01 0.5646E+00 0.2238E+00

1987 -0.1565E-01 0.1183E-02 -0.7475E+01 0.2250E+00 0.2247E+00

1988 -0.3354E-01 0.4397E-02 -0.4562E+01 0.7687E+00 0.2521E+00

1989 -0.6589E+00 0.2138E-01 -0.2159E+02 0.3711E+01 0.1868E+00

1990 -0.6673E-02 0.1193E-02 -0.3475E+01 0.1987E+00 0.2664E+00

1991 -0.4748E-01 0.3771E-02 -0.7320E+01 0.6961E+00 0.2324E+00

1992 -0.1161E+00 0.6617E-02 -0.1038E+02 0.1235E+01 0.2205E+00

1993 -0.8076E-01 0.3345E-02 -0.1566E+02 0.5964E+00 0.2112E+00

1994 -0.5187E-01 0.2024E-02 -0.1708E+02 0.3555E+00 0.2087E+00

1995 -0.1141E-01 0.7219E-03 -0.9344E+01 0.1335E+00 0.2262E+00

1996 -0.4561E-01 0.2539E-02 -0.1126E+02 0.4507E+00 0.2307E+00

1997 -0.3428E+00 0.1233E-01 -0.1941E+02 0.2109E+01 0.2046E+00

1998 -0.1619E+00 0.8525E-02 -0.1176E+02 0.1538E+01 0.2244E+00

1999 -0.1760E+00 0.6905E-02 -0.1739E+02 0.1188E+01 0.2135E+00

2000 -0.1625E+00 0.6149E-02 -0.1812E+02 0.1059E+01 0.2094E+00

2001 -0.1153E+00 0.5019E-02 -0.1413E+02 0.9311E+00 0.2068E+00

2002 -0.5819E-01 0.2621E-02 -0.1417E+02 0.4690E+00 0.2169E+00

2003 -0.7983E-01 0.3501E-02 -0.1473E+02 0.6217E+00 0.2166E+00

2004 -0.8658E-01 0.4258E-02 -0.1309E+02 0.7478E+00 0.2268E+00

2005 -0.8697E-01 0.3114E-02 -0.1827E+02 0.5629E+00 0.1932E+00

2006 -0.8295E-01 0.4062E-02 -0.1256E+02 0.7433E+00 0.2174E+00

2007 -0.1145E+00 0.4548E-02 -0.1655E+02 0.8067E+00 0.2083E+00

2008 -0.7583E-01 0.2185E-02 -0.1616E+02 0.5451E+00 0.1130E+00

Year 5. % Percentile 95. % Percentile

1978 0.431482E+00 0.113102E+01

1979 0.379464E+00 0.980853E+00

1980 0.691453E+00 0.179344E+01

1981 0.378278E+00 0.100320E+01

1982 0.236561E+00 0.600732E+00

1983 0.157420E+00 0.392914E+00

1984 0.345229E+00 0.887291E+00

1985 0.280877E+00 0.712360E+00

1986 0.310336E+00 0.714152E+00

1987 0.125666E+00 0.290912E+00

1988 0.452334E+00 0.106890E+01

- 101 -

1989 0.147685E+01 0.365714E+01

1990 0.109910E+00 0.281329E+00

1991 0.390160E+00 0.901544E+00

1992 0.639466E+00 0.148644E+01

1993 0.265327E+00 0.659181E+00

1994 0.153110E+00 0.387155E+00

1995 0.701961E-01 0.166243E+00

1996 0.227076E+00 0.557264E+00

1997 0.858295E+00 0.222761E+01

1998 0.758287E+00 0.185100E+01

1999 0.503832E+00 0.129828E+01

2000 0.432775E+00 0.113538E+01

2001 0.458678E+00 0.106079E+01

2002 0.217788E+00 0.538985E+00

2003 0.289249E+00 0.702530E+00

2004 0.352756E+00 0.897144E+00

2005 0.252400E+00 0.589110E+00

2006 0.359935E+00 0.875940E+00

2007 0.353158E+00 0.880522E+00

2008 0.312522E+00 0.506724E+00

Bootstrap Output Variable: Post-Recruit Biomass

Year NLLS Bootstrap Bootstrap C.V. For

Estimate Mean Std Error Bootstrap

1978 0.141963E+01 0.128048E+01 0.398571E+00 0.311266E+00

1979 0.289871E+01 0.260006E+01 0.769555E+00 0.295975E+00

1980 0.213768E+01 0.195519E+01 0.611873E+00 0.312949E+00

1981 0.566651E+01 0.505534E+01 0.146660E+01 0.290108E+00

1982 0.214428E+01 0.215038E+01 0.583191E+00 0.271204E+00

1983 0.243262E+01 0.214802E+01 0.669361E+00 0.311618E+00

1984 0.385339E+01 0.322290E+01 0.101029E+01 0.313473E+00

1985 0.284711E+01 0.270959E+01 0.834860E+00 0.308113E+00

1986 0.347002E+01 0.348681E+01 0.968778E+00 0.277841E+00

1987 0.262780E+01 0.234409E+01 0.745780E+00 0.318154E+00

1988 0.538671E+01 0.477629E+01 0.148415E+01 0.310733E+00

1989 0.965220E+01 0.816626E+01 0.247639E+01 0.303246E+00

1990 0.714834E+01 0.832841E+01 0.142196E+01 0.170737E+00

1991 0.607909E+01 0.513525E+01 0.168522E+01 0.328167E+00

1992 0.866971E+01 0.761081E+01 0.224577E+01 0.295076E+00

1993 0.588703E+01 0.528170E+01 0.169111E+01 0.320183E+00

1994 0.548541E+01 0.519395E+01 0.161752E+01 0.311424E+00

1995 0.550195E+01 0.532456E+01 0.156571E+01 0.294054E+00

1996 0.413368E+01 0.368486E+01 0.114114E+01 0.309684E+00

1997 0.506790E+01 0.454088E+01 0.139076E+01 0.306275E+00

1998 0.604999E+01 0.587693E+01 0.173962E+01 0.296008E+00

1999 0.549763E+01 0.501911E+01 0.158159E+01 0.315114E+00

2000 0.494702E+01 0.468383E+01 0.141864E+01 0.302880E+00

2001 0.417319E+01 0.403597E+01 0.120107E+01 0.297591E+00

2002 0.274421E+01 0.254487E+01 0.826187E+00 0.324648E+00

2003 0.258959E+01 0.238663E+01 0.752117E+00 0.315138E+00

2004 0.364719E+01 0.341698E+01 0.107258E+01 0.313896E+00

2005 0.451667E+01 0.404661E+01 0.123332E+01 0.304778E+00

2006 0.140995E+01 0.136573E+01 0.462129E+00 0.338375E+00

2007 0.495972E+01 0.446613E+01 0.132652E+01 0.297019E+00

2008 0.314799E+01 0.306666E+01 0.995493E+00 0.324618E+00

NLLS

Estimate C.V. For

Bias Bias Per Cent Corrected Corrected

Year Estimate Std. Error Bias For Bias Estimate

1978 -0.1391E+00 0.9440E-02 -0.9802E+01 0.1559E+01 0.2557E+00

1979 -0.2986E+00 0.1846E-01 -0.1030E+02 0.3197E+01 0.2407E+00

1980 -0.1825E+00 0.1428E-01 -0.8537E+01 0.2320E+01 0.2637E+00

1981 -0.6112E+00 0.3553E-01 -0.1079E+02 0.6278E+01 0.2336E+00

1982 0.6093E-02 0.1304E-01 0.2842E+00 0.2138E+01 0.2727E+00

1983 -0.2846E+00 0.1626E-01 -0.1170E+02 0.2717E+01 0.2463E+00

1984 -0.6305E+00 0.2663E-01 -0.1636E+02 0.4484E+01 0.2253E+00

1985 -0.1375E+00 0.1892E-01 -0.4830E+01 0.2985E+01 0.2797E+00

1986 0.1679E-01 0.2167E-01 0.4838E+00 0.3453E+01 0.2805E+00

1987 -0.2837E+00 0.1784E-01 -0.1080E+02 0.2912E+01 0.2561E+00

1988 -0.6104E+00 0.3589E-01 -0.1133E+02 0.5997E+01 0.2475E+00

1989 -0.1486E+01 0.6458E-01 -0.1539E+02 0.1114E+02 0.2223E+00

1990 0.1180E+01 0.4132E-01 0.1651E+02 0.5968E+01 0.2383E+00

1991 -0.9438E+00 0.4319E-01 -0.1553E+02 0.7023E+01 0.2400E+00

- 102 -

1992 -0.1059E+01 0.5552E-01 -0.1221E+02 0.9729E+01 0.2308E+00

1993 -0.6053E+00 0.4017E-01 -0.1028E+02 0.6492E+01 0.2605E+00

1994 -0.2915E+00 0.3675E-01 -0.5313E+01 0.5777E+01 0.2800E+00

1995 -0.1774E+00 0.3523E-01 -0.3224E+01 0.5679E+01 0.2757E+00

1996 -0.4488E+00 0.2742E-01 -0.1086E+02 0.4582E+01 0.2490E+00

1997 -0.5270E+00 0.3326E-01 -0.1040E+02 0.5595E+01 0.2486E+00

1998 -0.1731E+00 0.3909E-01 -0.2860E+01 0.6223E+01 0.2795E+00

1999 -0.4785E+00 0.3695E-01 -0.8704E+01 0.5976E+01 0.2647E+00

2000 -0.2632E+00 0.3226E-01 -0.5320E+01 0.5210E+01 0.2723E+00

2001 -0.1372E+00 0.2703E-01 -0.3288E+01 0.4310E+01 0.2786E+00

2002 -0.1993E+00 0.1900E-01 -0.7264E+01 0.2944E+01 0.2807E+00

2003 -0.2030E+00 0.1742E-01 -0.7838E+01 0.2793E+01 0.2693E+00

2004 -0.2302E+00 0.2453E-01 -0.6312E+01 0.3877E+01 0.2766E+00

2005 -0.4701E+00 0.2951E-01 -0.1041E+02 0.4987E+01 0.2473E+00

2006 -0.4422E-01 0.1038E-01 -0.3136E+01 0.1454E+01 0.3178E+00

2007 -0.4936E+00 0.3165E-01 -0.9952E+01 0.5453E+01 0.2433E+00

2008 -0.8134E-01 0.2233E-01 -0.2584E+01 0.3229E+01 0.3083E+00

Year 5. % Percentile 95. % Percentile

1978 0.761081E+00 0.198577E+01

1979 0.157721E+01 0.400320E+01

1980 0.111702E+01 0.302959E+01

1981 0.308139E+01 0.774435E+01

1982 0.134576E+01 0.320271E+01

1983 0.126298E+01 0.340998E+01

1984 0.189987E+01 0.512266E+01

1985 0.156230E+01 0.426770E+01

1986 0.216200E+01 0.531345E+01

1987 0.136692E+01 0.377233E+01

1988 0.279210E+01 0.745790E+01

1989 0.486339E+01 0.124833E+02

1990 0.618804E+01 0.107477E+02

1991 0.298373E+01 0.821271E+01

1992 0.454844E+01 0.117610E+02

1993 0.304000E+01 0.833548E+01

1994 0.303272E+01 0.821086E+01

1995 0.324668E+01 0.823682E+01

1996 0.217317E+01 0.578170E+01

1997 0.270611E+01 0.714794E+01

1998 0.358582E+01 0.912676E+01

1999 0.291180E+01 0.785025E+01

2000 0.281685E+01 0.732331E+01

2001 0.241426E+01 0.621137E+01

2002 0.144708E+01 0.406884E+01

2003 0.139668E+01 0.374937E+01

2004 0.201225E+01 0.539123E+01

2005 0.239942E+01 0.639619E+01

2006 0.758778E+00 0.215053E+01

2007 0.263031E+01 0.687311E+01

2008 0.179778E+01 0.496600E+01

Bootstrap Output Variable: Total Biomass

Year NLLS Bootstrap Bootstrap C.V. For

Estimate Mean Std Error Bootstrap

1978 0.224830E+01 0.200226E+01 0.500742E+00 0.250088E+00

1979 0.362267E+01 0.323465E+01 0.836104E+00 0.258483E+00

1980 0.349293E+01 0.311649E+01 0.783805E+00 0.251503E+00

1981 0.640960E+01 0.569810E+01 0.153035E+01 0.268572E+00

1982 0.255836E+01 0.253602E+01 0.604917E+00 0.238530E+00

1983 0.270249E+01 0.240453E+01 0.689408E+00 0.286712E+00

1984 0.453433E+01 0.379660E+01 0.107528E+01 0.283222E+00

1985 0.342614E+01 0.317682E+01 0.881494E+00 0.277477E+00

1986 0.399198E+01 0.396615E+01 0.973295E+00 0.245401E+00

1987 0.283711E+01 0.253775E+01 0.755646E+00 0.297762E+00

1988 0.612185E+01 0.547789E+01 0.153054E+01 0.279403E+00

1989 0.127039E+02 0.105591E+02 0.272470E+01 0.258044E+00

1990 0.734039E+01 0.851378E+01 0.139644E+01 0.164022E+00

1991 0.672771E+01 0.573641E+01 0.172748E+01 0.301144E+00

1992 0.978819E+01 0.861322E+01 0.230806E+01 0.267968E+00

1993 0.640267E+01 0.571657E+01 0.173506E+01 0.303514E+00

1994 0.578904E+01 0.544571E+01 0.163871E+01 0.300918E+00

1995 0.562403E+01 0.543523E+01 0.156874E+01 0.288624E+00

1996 0.453881E+01 0.404438E+01 0.117090E+01 0.289513E+00

1997 0.683406E+01 0.596421E+01 0.157237E+01 0.263634E+00

- 103 -

1998 0.742652E+01 0.709154E+01 0.184684E+01 0.260429E+00

1999 0.650976E+01 0.585523E+01 0.167381E+01 0.285866E+00

2000 0.584356E+01 0.541790E+01 0.149420E+01 0.275791E+00

2001 0.498900E+01 0.473650E+01 0.125543E+01 0.265054E+00

2002 0.315498E+01 0.289745E+01 0.861733E+00 0.297410E+00

2003 0.313145E+01 0.284866E+01 0.803999E+00 0.282238E+00

2004 0.430845E+01 0.399166E+01 0.112372E+01 0.281517E+00

2005 0.499259E+01 0.443556E+01 0.127164E+01 0.286692E+00

2006 0.207029E+01 0.194311E+01 0.535787E+00 0.275736E+00

2007 0.565187E+01 0.504374E+01 0.137679E+01 0.272970E+00

2008 0.361726E+01 0.346009E+01 0.103224E+01 0.298328E+00

NLLS

Estimate C.V. For

Bias Bias Per Cent Corrected Corrected

Year Estimate Std. Error Bias For Bias Estimate

1978 -0.2460E+00 0.1248E-01 -0.1094E+02 0.2494E+01 0.2008E+00

1979 -0.3880E+00 0.2061E-01 -0.1071E+02 0.4011E+01 0.2085E+00

1980 -0.3764E+00 0.1944E-01 -0.1078E+02 0.3869E+01 0.2026E+00

1981 -0.7115E+00 0.3774E-01 -0.1110E+02 0.7121E+01 0.2149E+00

1982 -0.2234E-01 0.1354E-01 -0.8731E+00 0.2581E+01 0.2344E+00

1983 -0.2980E+00 0.1679E-01 -0.1103E+02 0.3000E+01 0.2298E+00

1984 -0.7377E+00 0.2916E-01 -0.1627E+02 0.5272E+01 0.2040E+00

1985 -0.2493E+00 0.2048E-01 -0.7277E+01 0.3675E+01 0.2398E+00

1986 -0.2584E-01 0.2177E-01 -0.6472E+00 0.4018E+01 0.2422E+00

1987 -0.2994E+00 0.1818E-01 -0.1055E+02 0.3136E+01 0.2409E+00

1988 -0.6440E+00 0.3713E-01 -0.1052E+02 0.6766E+01 0.2262E+00

1989 -0.2145E+01 0.7755E-01 -0.1688E+02 0.1485E+02 0.1835E+00

1990 0.1173E+01 0.4079E-01 0.1599E+02 0.6167E+01 0.2264E+00

1991 -0.9913E+00 0.4454E-01 -0.1473E+02 0.7719E+01 0.2238E+00

1992 -0.1175E+01 0.5792E-01 -0.1200E+02 0.1096E+02 0.2105E+00

1993 -0.6861E+00 0.4172E-01 -0.1072E+02 0.7089E+01 0.2448E+00

1994 -0.3433E+00 0.3744E-01 -0.5931E+01 0.6132E+01 0.2672E+00

1995 -0.1888E+00 0.3533E-01 -0.3357E+01 0.5813E+01 0.2699E+00

1996 -0.4944E+00 0.2842E-01 -0.1089E+02 0.5033E+01 0.2326E+00

1997 -0.8698E+00 0.4018E-01 -0.1273E+02 0.7704E+01 0.2041E+00

1998 -0.3350E+00 0.4197E-01 -0.4511E+01 0.7761E+01 0.2379E+00

1999 -0.6545E+00 0.4019E-01 -0.1005E+02 0.7164E+01 0.2336E+00

2000 -0.4257E+00 0.3474E-01 -0.7284E+01 0.6269E+01 0.2383E+00

2001 -0.2525E+00 0.2863E-01 -0.5061E+01 0.5242E+01 0.2395E+00

2002 -0.2575E+00 0.2011E-01 -0.8163E+01 0.3413E+01 0.2525E+00

2003 -0.2828E+00 0.1906E-01 -0.9031E+01 0.3414E+01 0.2355E+00

2004 -0.3168E+00 0.2611E-01 -0.7353E+01 0.4625E+01 0.2430E+00

2005 -0.5570E+00 0.3104E-01 -0.1116E+02 0.5550E+01 0.2291E+00

2006 -0.1272E+00 0.1231E-01 -0.6143E+01 0.2197E+01 0.2438E+00

2007 -0.6081E+00 0.3366E-01 -0.1076E+02 0.6260E+01 0.2199E+00

2008 -0.1572E+00 0.2335E-01 -0.4345E+01 0.3774E+01 0.2735E+00

Year 5. % Percentile 95. % Percentile

1978 0.130188E+01 0.287566E+01

1979 0.213595E+01 0.476247E+01

1980 0.205148E+01 0.455346E+01

1981 0.358273E+01 0.852908E+01

1982 0.173494E+01 0.361526E+01

1983 0.150953E+01 0.368021E+01

1984 0.238761E+01 0.580404E+01

1985 0.195964E+01 0.486552E+01

1986 0.267015E+01 0.578232E+01

1987 0.154226E+01 0.398710E+01

1988 0.342752E+01 0.827152E+01

1989 0.682151E+01 0.153060E+02

1990 0.643630E+01 0.109146E+02

1991 0.355517E+01 0.884973E+01

1992 0.550155E+01 0.128571E+02

1993 0.341647E+01 0.882654E+01

1994 0.325245E+01 0.851810E+01

1995 0.335680E+01 0.835624E+01

1996 0.249227E+01 0.618651E+01

1997 0.384446E+01 0.891979E+01

1998 0.465559E+01 0.105476E+02

1999 0.361676E+01 0.888379E+01

2000 0.342663E+01 0.816127E+01

2001 0.304246E+01 0.705550E+01

2002 0.173489E+01 0.449580E+01

2003 0.180971E+01 0.435973E+01

- 104 -

2004 0.251138E+01 0.607586E+01

2005 0.274122E+01 0.687970E+01

2006 0.124034E+01 0.289421E+01

2007 0.317954E+01 0.763694E+01

2008 0.214143E+01 0.543957E+01

Bootstrap Output Variable: Fishing Mortality

Year NLLS Bootstrap Bootstrap C.V. For

Estimate Mean Std Error Bootstrap

1978 0.355165E+00 0.336667E+00 0.297424E+00 0.883436E+00

1979 0.652634E+00 0.638419E+00 0.277163E+00 0.434139E+00

1980 0.570908E+00 0.537802E+00 0.308995E+00 0.574551E+00

1981 0.105289E+01 0.926240E+00 0.275362E+00 0.297291E+00

1982 -0.716637E-01 0.427499E-01 0.268424E+00 0.627895E+01

1983 -0.296746E+00 -0.174996E+00 0.280108E+00 -0.160065E+01

1984 0.101354E+01 0.903018E+00 0.285394E+00 0.316045E+00

1985 0.126628E+01 0.106345E+01 0.298239E+00 0.280446E+00

1986 0.458428E+00 0.553440E+00 0.270513E+00 0.488785E+00

1987 0.127709E+00 0.184519E+00 0.276388E+00 0.149788E+01

1988 -0.793868E-01 0.407559E-01 0.276455E+00 0.678320E+01

1989 0.186006E+01 0.145384E+01 0.286048E+00 0.196753E+00

1990 -0.412298E-01 0.265054E+00 0.278429E+00 0.105046E+01

1991 0.121537E+00 0.172750E+00 0.280944E+00 0.162631E+01

1992 0.635220E+00 0.652455E+00 0.266240E+00 0.408059E+00

1993 0.100645E+01 0.914041E+00 0.283142E+00 0.309770E+00

1994 0.117547E+01 0.104626E+01 0.287703E+00 0.274982E+00

1995 0.456530E+00 0.522745E+00 0.258942E+00 0.495351E+00

1996 0.473142E+00 0.479958E+00 0.274593E+00 0.572118E+00

1997 0.129731E+01 0.112676E+01 0.303735E+00 0.269565E+00

1998 0.681514E+00 0.693093E+00 0.279392E+00 0.403109E+00

1999 0.110106E+01 0.989901E+00 0.288907E+00 0.291855E+00

2000 0.129060E+01 0.115872E+01 0.290618E+00 0.250810E+00

2001 0.990313E+00 0.969764E+00 0.277673E+00 0.286330E+00

2002 0.759197E+00 0.723431E+00 0.284935E+00 0.393866E+00

2003 0.780446E+00 0.713455E+00 0.287596E+00 0.403104E+00

2004 0.643127E+00 0.638036E+00 0.281301E+00 0.440886E+00

2005 0.152068E+01 0.140502E+01 0.272823E+00 0.194177E+00

2006 0.641518E+00 0.628049E+00 0.289490E+00 0.460935E+00

2007 0.119787E+01 0.107984E+01 0.294307E+00 0.272546E+00

NLLS

Estimate C.V. For

Bias Bias Per Cent Corrected Corrected

Year Estimate Std. Error Bias For Bias Estimate

1978 -0.1850E-01 0.6663E-02 -0.5208E+01 0.3737E+00 0.7960E+00

1979 -0.1422E-01 0.6206E-02 -0.2178E+01 0.6668E+00 0.4156E+00

1980 -0.3311E-01 0.6949E-02 -0.5799E+01 0.6040E+00 0.5116E+00

1981 -0.1266E+00 0.6778E-02 -0.1203E+02 0.1180E+01 0.2334E+00

1982 0.1144E+00 0.6525E-02 -0.1597E+03 -0.1861E+00 -0.1443E+01

1983 0.1217E+00 0.6830E-02 -0.4103E+02 -0.4185E+00 -0.6693E+00

1984 -0.1105E+00 0.6844E-02 -0.1090E+02 0.1124E+01 0.2539E+00

1985 -0.2028E+00 0.8066E-02 -0.1602E+02 0.1469E+01 0.2030E+00

1986 0.9501E-01 0.6411E-02 0.2073E+02 0.3634E+00 0.7444E+00

1987 0.5681E-01 0.6309E-02 0.4448E+02 0.7090E-01 0.3898E+01

1988 0.1201E+00 0.6741E-02 -0.1513E+03 -0.1995E+00 -0.1386E+01

1989 -0.4062E+00 0.1111E-01 -0.2184E+02 0.2266E+01 0.1262E+00

1990 0.3063E+00 0.9257E-02 -0.7429E+03 -0.3475E+00 -0.8012E+00

1991 0.5121E-01 0.6386E-02 0.4214E+02 0.7032E-01 0.3995E+01

1992 0.1723E-01 0.5966E-02 0.2713E+01 0.6180E+00 0.4308E+00

1993 -0.9241E-01 0.6660E-02 -0.9182E+01 0.1099E+01 0.2577E+00

1994 -0.1292E+00 0.7053E-02 -0.1099E+02 0.1305E+01 0.2205E+00

1995 0.6621E-01 0.5977E-02 0.1450E+02 0.3903E+00 0.6634E+00

1996 0.6816E-02 0.6142E-02 0.1441E+01 0.4663E+00 0.5888E+00

1997 -0.1706E+00 0.7790E-02 -0.1315E+02 0.1468E+01 0.2069E+00

1998 0.1158E-01 0.6253E-02 0.1699E+01 0.6699E+00 0.4170E+00

1999 -0.1112E+00 0.6922E-02 -0.1010E+02 0.1212E+01 0.2383E+00

2000 -0.1319E+00 0.7137E-02 -0.1022E+02 0.1422E+01 0.2043E+00

2001 -0.2055E-01 0.6226E-02 -0.2075E+01 0.1011E+01 0.2747E+00

2002 -0.3577E-01 0.6421E-02 -0.4711E+01 0.7950E+00 0.3584E+00

2003 -0.6699E-01 0.6603E-02 -0.8584E+01 0.8474E+00 0.3394E+00

2004 -0.5091E-02 0.6291E-02 -0.7916E+00 0.6482E+00 0.4340E+00

2005 -0.1157E+00 0.6626E-02 -0.7606E+01 0.1636E+01 0.1667E+00

2006 -0.1347E-01 0.6480E-02 -0.2100E+01 0.6550E+00 0.4420E+00

2007 -0.1180E+00 0.7091E-02 -0.9853E+01 0.1316E+01 0.2237E+00

- 105 -

Year 5. % Percentile 95. % Percentile

1978 -0.153434E+00 0.830322E+00

1979 0.181412E+00 0.109207E+01

1980 0.222595E-01 0.104113E+01

1981 0.477901E+00 0.138479E+01

1982 -0.400999E+00 0.481566E+00

1983 -0.637354E+00 0.290312E+00

1984 0.447107E+00 0.139022E+01

1985 0.568434E+00 0.153689E+01

1986 0.102911E+00 0.988847E+00

1987 -0.260139E+00 0.635599E+00

1988 -0.398175E+00 0.497893E+00

1989 0.991081E+00 0.192117E+01

1990 -0.190538E+00 0.723091E+00

1991 -0.290517E+00 0.634181E+00

1992 0.204520E+00 0.107669E+01

1993 0.427989E+00 0.136669E+01

1994 0.579353E+00 0.153000E+01

1995 0.904320E-01 0.947435E+00

1996 0.408959E-01 0.940752E+00

1997 0.647025E+00 0.162647E+01

1998 0.217060E+00 0.115643E+01

1999 0.513157E+00 0.145935E+01

2000 0.687618E+00 0.164581E+01

2001 0.519247E+00 0.143278E+01

2002 0.241965E+00 0.120313E+01

2003 0.253139E+00 0.118173E+01

2004 0.165762E+00 0.108038E+01

2005 0.950477E+00 0.185348E+01

2006 0.168402E+00 0.111522E+01

2007 0.609026E+00 0.157176E+01

Bootstrap Output Variable: Total Mortality

Year NLLS Bootstrap Bootstrap C.V. For

Estimate Mean Std Error Bootstrap

1978 0.115517E+01 0.113667E+01 0.297424E+00 0.261663E+00

1979 0.145263E+01 0.143842E+01 0.277163E+00 0.192686E+00

1980 0.137091E+01 0.133780E+01 0.308995E+00 0.230972E+00

1981 0.185289E+01 0.172624E+01 0.275362E+00 0.159516E+00

1982 0.728336E+00 0.842750E+00 0.268424E+00 0.318510E+00

1983 0.503254E+00 0.625004E+00 0.280108E+00 0.448170E+00

1984 0.181354E+01 0.170302E+01 0.285394E+00 0.167581E+00

1985 0.206628E+01 0.186345E+01 0.298239E+00 0.160047E+00

1986 0.125843E+01 0.135344E+01 0.270513E+00 0.199871E+00

1987 0.927709E+00 0.984519E+00 0.276388E+00 0.280734E+00

1988 0.720613E+00 0.840756E+00 0.276455E+00 0.328817E+00

1989 0.266006E+01 0.225384E+01 0.286048E+00 0.126916E+00

1990 0.758770E+00 0.106505E+01 0.278429E+00 0.261423E+00

1991 0.921537E+00 0.972750E+00 0.280944E+00 0.288815E+00

1992 0.143522E+01 0.145245E+01 0.266240E+00 0.183303E+00

1993 0.180645E+01 0.171404E+01 0.283142E+00 0.165190E+00

1994 0.197547E+01 0.184626E+01 0.287703E+00 0.155830E+00

1995 0.125653E+01 0.132275E+01 0.258942E+00 0.195761E+00

1996 0.127314E+01 0.127996E+01 0.274593E+00 0.214533E+00

1997 0.209731E+01 0.192676E+01 0.303735E+00 0.157640E+00

1998 0.148151E+01 0.149309E+01 0.279392E+00 0.187123E+00

1999 0.190106E+01 0.178990E+01 0.288907E+00 0.161410E+00

2000 0.209060E+01 0.195872E+01 0.290618E+00 0.148372E+00

2001 0.179031E+01 0.176976E+01 0.277673E+00 0.156898E+00

2002 0.155920E+01 0.152343E+01 0.284935E+00 0.187035E+00

2003 0.158045E+01 0.151345E+01 0.287596E+00 0.190026E+00

2004 0.144313E+01 0.143804E+01 0.281301E+00 0.195615E+00

2005 0.232068E+01 0.220502E+01 0.272823E+00 0.123728E+00

2006 0.144152E+01 0.142805E+01 0.289490E+00 0.202717E+00

2007 0.199787E+01 0.187984E+01 0.294307E+00 0.156559E+00

NLLS

Estimate C.V. For

Bias Bias Per Cent Corrected Corrected

Year Estimate Std. Error Bias For Bias Estimate

1978 -0.1850E-01 0.6663E-02 -0.1601E+01 0.1174E+01 0.2534E+00

1979 -0.1422E-01 0.6206E-02 -0.9786E+00 0.1467E+01 0.1890E+00

- 106 -

1980 -0.3311E-01 0.6949E-02 -0.2415E+01 0.1404E+01 0.2201E+00

1981 -0.1266E+00 0.6778E-02 -0.6835E+01 0.1980E+01 0.1391E+00

1982 0.1144E+00 0.6525E-02 0.1571E+02 0.6139E+00 0.4372E+00

1983 0.1217E+00 0.6830E-02 0.2419E+02 0.3815E+00 0.7342E+00

1984 -0.1105E+00 0.6844E-02 -0.6094E+01 0.1924E+01 0.1483E+00

1985 -0.2028E+00 0.8066E-02 -0.9816E+01 0.2269E+01 0.1314E+00

1986 0.9501E-01 0.6411E-02 0.7550E+01 0.1163E+01 0.2325E+00

1987 0.5681E-01 0.6309E-02 0.6124E+01 0.8709E+00 0.3174E+00

1988 0.1201E+00 0.6741E-02 0.1667E+02 0.6005E+00 0.4604E+00

1989 -0.4062E+00 0.1111E-01 -0.1527E+02 0.3066E+01 0.9329E-01

1990 0.3063E+00 0.9257E-02 0.4037E+02 0.4525E+00 0.6153E+00

1991 0.5121E-01 0.6386E-02 0.5557E+01 0.8703E+00 0.3228E+00

1992 0.1723E-01 0.5966E-02 0.1201E+01 0.1418E+01 0.1878E+00

1993 -0.9241E-01 0.6660E-02 -0.5116E+01 0.1899E+01 0.1491E+00

1994 -0.1292E+00 0.7053E-02 -0.6541E+01 0.2105E+01 0.1367E+00

1995 0.6621E-01 0.5977E-02 0.5270E+01 0.1190E+01 0.2175E+00

1996 0.6816E-02 0.6142E-02 0.5354E+00 0.1266E+01 0.2168E+00

1997 -0.1706E+00 0.7790E-02 -0.8132E+01 0.2268E+01 0.1339E+00

1998 0.1158E-01 0.6253E-02 0.7816E+00 0.1470E+01 0.1901E+00

1999 -0.1112E+00 0.6922E-02 -0.5847E+01 0.2012E+01 0.1436E+00

2000 -0.1319E+00 0.7137E-02 -0.6308E+01 0.2222E+01 0.1308E+00

2001 -0.2055E-01 0.6226E-02 -0.1148E+01 0.1811E+01 0.1533E+00

2002 -0.3577E-01 0.6421E-02 -0.2294E+01 0.1595E+01 0.1786E+00

2003 -0.6699E-01 0.6603E-02 -0.4239E+01 0.1647E+01 0.1746E+00

2004 -0.5091E-02 0.6291E-02 -0.3528E+00 0.1448E+01 0.1942E+00

2005 -0.1157E+00 0.6626E-02 -0.4984E+01 0.2436E+01 0.1120E+00

2006 -0.1347E-01 0.6480E-02 -0.9344E+00 0.1455E+01 0.1990E+00

2007 -0.1180E+00 0.7091E-02 -0.5908E+01 0.2116E+01 0.1391E+00

Year 5. % Percentile 95. % Percentile

1978 0.646566E+00 0.163032E+01

1979 0.981412E+00 0.189207E+01

1980 0.822260E+00 0.184113E+01

1981 0.127790E+01 0.218479E+01

1982 0.399001E+00 0.128157E+01

1983 0.162646E+00 0.109031E+01

1984 0.124711E+01 0.219022E+01

1985 0.136843E+01 0.233689E+01

1986 0.902911E+00 0.178885E+01

1987 0.539861E+00 0.143560E+01

1988 0.401825E+00 0.129789E+01

1989 0.179108E+01 0.272117E+01

1990 0.609462E+00 0.152309E+01

1991 0.509483E+00 0.143418E+01

1992 0.100452E+01 0.187669E+01

1993 0.122799E+01 0.216669E+01

1994 0.137935E+01 0.233000E+01

1995 0.890432E+00 0.174744E+01

1996 0.840896E+00 0.174075E+01

1997 0.144702E+01 0.242647E+01

1998 0.101706E+01 0.195643E+01

1999 0.131316E+01 0.225935E+01

2000 0.148762E+01 0.244581E+01

2001 0.131925E+01 0.223278E+01

2002 0.104197E+01 0.200313E+01

2003 0.105314E+01 0.198173E+01

2004 0.965762E+00 0.188038E+01

2005 0.175048E+01 0.265348E+01

2006 0.968402E+00 0.191522E+01

2007 0.140903E+01 0.237176E+01

Bootstrap Output Variable: F Derived From Harvest Rate

Year NLLS Bootstrap Bootstrap C.V. For

Estimate Mean Std Error Bootstrap

1978 0.143157E+00 0.179084E+00 0.511837E-01 0.285808E+00

1979 0.430304E+00 0.544287E+00 0.160207E+00 0.294342E+00

1980 0.118675E+00 0.151480E+00 0.458264E-01 0.302525E+00

1981 0.141989E+00 0.173944E+00 0.440343E-01 0.253151E+00

1982 0.729942E+00 0.830045E+00 0.231161E+00 0.278493E+00

1983 0.488543E+00 0.585001E+00 0.168011E+00 0.287198E+00

1984 0.322654E+00 0.433785E+00 0.135277E+00 0.311852E+00

1985 0.252977E+00 0.348788E+00 0.111124E+00 0.318600E+00

1986 0.109867E+01 0.131603E+01 0.387947E+00 0.294786E+00

1987 0.646918E+00 0.797624E+00 0.243907E+00 0.305792E+00

- 107 -

1988 0.608363E+00 0.726376E+00 0.213879E+00 0.294447E+00

1989 0.128998E+00 0.179050E+00 0.510553E-01 0.285145E+00

1990 0.218484E+01 0.184813E+01 0.395763E+00 0.214142E+00

1991 0.572725E+00 0.712788E+00 0.221723E+00 0.311064E+00

1992 0.778485E+00 0.102199E+01 0.319651E+00 0.312774E+00

1993 0.406065E+00 0.547630E+00 0.182068E+00 0.332465E+00

1994 0.377080E+00 0.512068E+00 0.166387E+00 0.324931E+00

1995 0.830916E+00 0.101971E+01 0.314847E+00 0.308763E+00

1996 0.561225E+00 0.726324E+00 0.231448E+00 0.318656E+00

1997 0.200545E+00 0.275094E+00 0.835300E-01 0.303641E+00

1998 0.554481E+00 0.694422E+00 0.217452E+00 0.313142E+00

1999 0.285901E+00 0.383740E+00 0.117966E+00 0.307412E+00

2000 0.304117E+00 0.408655E+00 0.127394E+00 0.311741E+00

2001 0.789362E+00 0.105985E+01 0.362093E+00 0.341646E+00

2002 0.452112E+00 0.589677E+00 0.190271E+00 0.322669E+00

2003 0.403568E+00 0.531538E+00 0.165241E+00 0.310874E+00

2004 0.458921E+00 0.595571E+00 0.193404E+00 0.324737E+00

2005 0.827553E+00 0.125263E+01 0.487412E+00 0.389112E+00

2006 0.405109E+00 0.524920E+00 0.173662E+00 0.330834E+00

2007 0.497301E+00 0.681298E+00 0.230507E+00 0.338334E+00

NLLS

Estimate C.V. For

Bias Bias Per Cent Corrected Corrected

Year Estimate Std. Error Bias For Bias Estimate

1978 0.3593E-01 0.1398E-02 0.2510E+02 0.1072E+00 0.4773E+00

1979 0.1140E+00 0.4397E-02 0.2649E+02 0.3163E+00 0.5065E+00

1980 0.3280E-01 0.1260E-02 0.2764E+02 0.8587E-01 0.5337E+00

1981 0.3196E-01 0.1217E-02 0.2251E+02 0.1100E+00 0.4002E+00

1982 0.1001E+00 0.5633E-02 0.1371E+02 0.6298E+00 0.3670E+00

1983 0.9646E-01 0.4332E-02 0.1974E+02 0.3921E+00 0.4285E+00

1984 0.1111E+00 0.3915E-02 0.3444E+02 0.2115E+00 0.6395E+00

1985 0.9581E-01 0.3281E-02 0.3787E+02 0.1572E+00 0.7070E+00

1986 0.2174E+00 0.9944E-02 0.1978E+02 0.8813E+00 0.4402E+00

1987 0.1507E+00 0.6411E-02 0.2330E+02 0.4962E+00 0.4915E+00

1988 0.1180E+00 0.5463E-02 0.1940E+02 0.4904E+00 0.4362E+00

1989 0.5005E-01 0.1599E-02 0.3880E+02 0.7895E-01 0.6467E+00

1990 -0.3367E+00 0.1162E-01 -0.1541E+02 0.2522E+01 0.1570E+00

1991 0.1401E+00 0.5865E-02 0.2446E+02 0.4327E+00 0.5125E+00

1992 0.2435E+00 0.8986E-02 0.3128E+02 0.5350E+00 0.5975E+00

1993 0.1416E+00 0.5157E-02 0.3486E+02 0.2645E+00 0.6883E+00

1994 0.1350E+00 0.4791E-02 0.3580E+02 0.2421E+00 0.6873E+00

1995 0.1888E+00 0.8209E-02 0.2272E+02 0.6421E+00 0.4903E+00

1996 0.1651E+00 0.6358E-02 0.2942E+02 0.3961E+00 0.5843E+00

1997 0.7455E-01 0.2504E-02 0.3717E+02 0.1260E+00 0.6630E+00

1998 0.1399E+00 0.5783E-02 0.2524E+02 0.4145E+00 0.5246E+00

1999 0.9784E-01 0.3427E-02 0.3422E+02 0.1881E+00 0.6273E+00

2000 0.1045E+00 0.3685E-02 0.3437E+02 0.1996E+00 0.6383E+00

2001 0.2705E+00 0.1011E-01 0.3427E+02 0.5189E+00 0.6978E+00

2002 0.1376E+00 0.5251E-02 0.3043E+02 0.3145E+00 0.6049E+00

2003 0.1280E+00 0.4674E-02 0.3171E+02 0.2756E+00 0.5996E+00

2004 0.1366E+00 0.5296E-02 0.2978E+02 0.3223E+00 0.6001E+00

2005 0.4251E+00 0.1446E-01 0.5137E+02 0.4025E+00 0.1211E+01

2006 0.1198E+00 0.4718E-02 0.2957E+02 0.2853E+00 0.6087E+00

2007 0.1840E+00 0.6596E-02 0.3700E+02 0.3133E+00 0.7357E+00

Year 5. % Percentile 95. % Percentile

1978 0.106243E+00 0.270618E+00

1979 0.326766E+00 0.849181E+00

1980 0.903503E-01 0.233268E+00

1981 0.111331E+00 0.252967E+00

1982 0.498773E+00 0.123343E+01

1983 0.348216E+00 0.896870E+00

1984 0.252547E+00 0.679871E+00

1985 0.202420E+00 0.556278E+00

1986 0.733472E+00 0.202854E+01

1987 0.453193E+00 0.125089E+01

1988 0.416454E+00 0.112257E+01

1989 0.109398E+00 0.266277E+00

1990 0.124312E+01 0.254285E+01

1991 0.402175E+00 0.112826E+01

1992 0.568660E+00 0.160856E+01

1993 0.311167E+00 0.878038E+00

1994 0.288652E+00 0.820683E+00

1995 0.583809E+00 0.158299E+01

- 108 -

1996 0.406961E+00 0.114150E+01

1997 0.157782E+00 0.426730E+00

1998 0.402485E+00 0.110392E+01

1999 0.220489E+00 0.593994E+00

2000 0.237322E+00 0.644921E+00

2001 0.571195E+00 0.172952E+01

2002 0.334378E+00 0.953820E+00

2003 0.304627E+00 0.827454E+00

2004 0.334051E+00 0.956652E+00

2005 0.635166E+00 0.217952E+01

2006 0.293571E+00 0.848987E+00

2007 0.383701E+00 0.107926E+01

Bootstrap Output Variable: Harvest Estimate

Year NLLS Bootstrap Bootstrap C.V. For

Estimate Mean Std Error Bootstrap

1978 0.926801E-01 0.113543E+00 0.297610E-01 0.262112E+00

1979 0.247555E+00 0.294861E+00 0.662948E-01 0.224834E+00

1980 0.776314E-01 0.971877E-01 0.271442E-01 0.279296E+00

1981 0.919696E-01 0.110673E+00 0.257339E-01 0.232522E+00

1982 0.373788E+00 0.402251E+00 0.765078E-01 0.190199E+00

1983 0.274624E+00 0.311879E+00 0.680181E-01 0.218091E+00

1984 0.193878E+00 0.245674E+00 0.616241E-01 0.250837E+00

1985 0.156427E+00 0.204774E+00 0.545152E-01 0.266221E+00

1986 0.491988E+00 0.533780E+00 0.893240E-01 0.167342E+00

1987 0.341901E+00 0.390040E+00 0.819452E-01 0.210094E+00

1988 0.326331E+00 0.365686E+00 0.770019E-01 0.210568E+00

1989 0.840158E-01 0.113529E+00 0.295644E-01 0.260413E+00

1990 0.694979E+00 0.639748E+00 0.624589E-01 0.976303E-01

1991 0.311488E+00 0.360097E+00 0.795094E-01 0.220800E+00

1992 0.391447E+00 0.458872E+00 0.891680E-01 0.194320E+00

1993 0.235891E+00 0.295096E+00 0.740213E-01 0.250838E+00

1994 0.221627E+00 0.280246E+00 0.704731E-01 0.251468E+00

1995 0.409748E+00 0.458537E+00 0.878284E-01 0.191541E+00

1996 0.306604E+00 0.364594E+00 0.822914E-01 0.225707E+00

1997 0.126740E+00 0.166975E+00 0.441915E-01 0.264659E+00

1998 0.303718E+00 0.353326E+00 0.786622E-01 0.222634E+00

1999 0.174400E+00 0.222103E+00 0.564632E-01 0.254221E+00

2000 0.184130E+00 0.233928E+00 0.595039E-01 0.254369E+00

2001 0.395308E+00 0.467368E+00 0.960561E-01 0.205526E+00

2002 0.257847E+00 0.312637E+00 0.748108E-01 0.239289E+00

2003 0.234676E+00 0.288950E+00 0.695519E-01 0.240706E+00

2004 0.261022E+00 0.314903E+00 0.760055E-01 0.241362E+00

2005 0.408597E+00 0.511408E+00 0.109286E+00 0.213695E+00

2006 0.235426E+00 0.285570E+00 0.724655E-01 0.253757E+00

2007 0.278582E+00 0.347526E+00 0.819302E-01 0.235753E+00

NLLS

Estimate C.V. For

Bias Bias Per Cent Corrected Corrected

Year Estimate Std. Error Bias For Bias Estimate

1978 0.2086E-01 0.8128E-03 0.2251E+02 0.7182E-01 0.4144E+00

1979 0.4731E-01 0.1821E-02 0.1911E+02 0.2002E+00 0.3311E+00

1980 0.1956E-01 0.7481E-03 0.2519E+02 0.5808E-01 0.4674E+00

1981 0.1870E-01 0.7114E-03 0.2034E+02 0.7327E-01 0.3512E+00

1982 0.2846E-01 0.1825E-02 0.7615E+01 0.3453E+00 0.2216E+00

1983 0.3726E-01 0.1734E-02 0.1357E+02 0.2374E+00 0.2865E+00

1984 0.5180E-01 0.1800E-02 0.2672E+02 0.1421E+00 0.4337E+00

1985 0.4835E-01 0.1630E-02 0.3091E+02 0.1081E+00 0.5044E+00

1986 0.4179E-01 0.2205E-02 0.8494E+01 0.4502E+00 0.1984E+00

1987 0.4814E-01 0.2125E-02 0.1408E+02 0.2938E+00 0.2790E+00

1988 0.3936E-01 0.1934E-02 0.1206E+02 0.2870E+00 0.2683E+00

1989 0.2951E-01 0.9342E-03 0.3513E+02 0.5450E-01 0.5424E+00

1990 -0.5523E-01 0.1865E-02 -0.7947E+01 0.7502E+00 0.8326E-01

1991 0.4861E-01 0.2084E-02 0.1561E+02 0.2629E+00 0.3025E+00

1992 0.6743E-01 0.2500E-02 0.1722E+02 0.3240E+00 0.2752E+00

1993 0.5920E-01 0.2120E-02 0.2510E+02 0.1767E+00 0.4189E+00

1994 0.5862E-01 0.2050E-02 0.2645E+02 0.1630E+00 0.4323E+00

1995 0.4879E-01 0.2247E-02 0.1191E+02 0.3610E+00 0.2433E+00

1996 0.5799E-01 0.2251E-02 0.1891E+02 0.2486E+00 0.3310E+00

1997 0.4024E-01 0.1337E-02 0.3175E+02 0.8650E-01 0.5109E+00

1998 0.4961E-01 0.2080E-02 0.1633E+02 0.2541E+00 0.3096E+00

1999 0.4770E-01 0.1653E-02 0.2735E+02 0.1267E+00 0.4457E+00

2000 0.4980E-01 0.1735E-02 0.2704E+02 0.1343E+00 0.4430E+00

- 109 -

2001 0.7206E-01 0.2685E-02 0.1823E+02 0.3232E+00 0.2972E+00

2002 0.5479E-01 0.2074E-02 0.2125E+02 0.2031E+00 0.3684E+00

2003 0.5427E-01 0.1973E-02 0.2313E+02 0.1804E+00 0.3855E+00

2004 0.5388E-01 0.2083E-02 0.2064E+02 0.2071E+00 0.3669E+00

2005 0.1028E+00 0.3355E-02 0.2516E+02 0.3058E+00 0.3574E+00

2006 0.5014E-01 0.1971E-02 0.2130E+02 0.1853E+00 0.3911E+00

2007 0.6894E-01 0.2395E-02 0.2475E+02 0.2096E+00 0.3908E+00

Year 5. % Percentile 95. % Percentile

1978 0.698672E-01 0.166120E+00

1979 0.196019E+00 0.415941E+00

1980 0.598196E-01 0.145424E+00

1981 0.730552E-01 0.156421E+00

1982 0.279244E+00 0.527185E+00

1983 0.207070E+00 0.431685E+00

1984 0.156189E+00 0.354819E+00

1985 0.127825E+00 0.304488E+00

1986 0.375096E+00 0.674784E+00

1987 0.258352E+00 0.531477E+00

1988 0.240920E+00 0.498507E+00

1989 0.718455E-01 0.163748E+00

1990 0.529573E+00 0.733804E+00

1991 0.233997E+00 0.500040E+00

1992 0.309767E+00 0.607782E+00

1993 0.187855E+00 0.425540E+00

1994 0.175880E+00 0.406237E+00

1995 0.316152E+00 0.602991E+00

1996 0.236327E+00 0.503584E+00

1997 0.101520E+00 0.245850E+00

1998 0.234148E+00 0.493432E+00

1999 0.138189E+00 0.320399E+00

2000 0.147702E+00 0.341106E+00

2001 0.310841E+00 0.629243E+00

2002 0.199964E+00 0.449706E+00

2003 0.184400E+00 0.408563E+00

2004 0.199795E+00 0.450581E+00

2005 0.337207E+00 0.694328E+00

2006 0.178516E+00 0.415876E+00

2007 0.224916E+00 0.486603E+00

Bootstrap Output Variable: Catchability (Q)

NLLS Bootstrap Bootstrap C.V. For

Estimate Mean Std Error NLLS Soln.

0.3868E-01 0.4718E-01 0.6800E-02 0.1441E+00

NLLS

Estimate C.V. For

Bias Bias Per Cent Corrected Corrected

Estimate Std. Error Bias For Bias Estimate

0.8492E-02 0.2433E-03 0.2195E+02 0.3019E-01 0.2252E+00

5. % Percentile 95. % Percentile

0.357231E-01 0.579396E-01